ICMS

Jul 9, 2007 - Jul 13, 2007

ICMS, 14 India Street, Edinburgh

Organisers

Name	Institution
Cairns, Andrew	Heriot-Watt University
Frittelli, Marco	Università degli Studi di Milano
Hobson, David	University of Warwick
Monoyios, Michael	University of Oxford
Schweizer, Martin	ETH Zurich

Short Report

Much of the research presented fell naturally into broad themes, such as illiquid markets, transaction costs (TC), incomplete information, credit risk, and analysis of risk preferences such as forward utilities and risk measures. Talks on the same theme were often grouped together. Many delegates commented that they liked this format.

There were talks on other areas, such as problems related to optimal stopping, and on modelling the observed implied volatility surface of market option prices.

The common theme was the extension of classical, perfect models of financial markets to incorporate one or more realistic and important market imperfections. The practical importance of such research is that it is essential to understanding how market failures can arise, and how to deal with the resulting risks. The recent turmoil in financial markets has arisen due to defaults on home loans in the United States (and is thus an instance of credit risk), and has resulted in lack of liquidity in interbank lending markets. The practical importance of the research therefore cannot be overstated.

The mathematical challenges involve techniques of functional and stochastic analysis, new techniques of stochastic control such as backward stochastic differential equations (BSDEs), and techniques of singular control, impulse control, and numerical and asymptotic analysis of partial differential equations (PDEs), often in high dimensions.

It is difficult to pick a single highlight, but the research on transaction costs, by Jan Kallsen, and on the dynamics of risk preferences, by Thaleia Zariphopoulou, generated a great deal of discussion and potential for future collaboration.

Participants list and links to available presentations are further down this page.

Download the pdf file of the full report

Original Details

The aims of the meeting are to build on the successes of the recent Developments in Quantitative Finance (DQF) programme at the Isaac Newton Institute for Mathematical Sciences (INIMS), Cambridge, by inviting some of the participants of that programme to reconvene, to further the advances and achievements of that programme and to describe more recent progress.

There has been a major expansion in the number of researchers working in the field of Financial Mathematics over recent years, and a further objective is to provide a forum for UK academics who are early in their career to listen to the most recent research and to present their work to an audience of senior researchers.

The outcomes of the meeting are expected to be progress in understanding the applications of the above mathematical techniques (robust control, partial differential equations, backward stochastic differential equations, martingale methods, convex duality techniques) to the management of new types of risk associated with the increasingly sophisticated products being offered by financial institutions, as well as to the computational challenges of valuing new products dependent on a large number of correlated assets. The interaction between distinguished senior academics and younger UK-based researchers will be a major stimulus to the UK Financial Mathematics community.

Arrangements

Participation
Participation is by invitation only. The workshop will begin with registration and coffee on Monday 9 July and finish on Friday 13 July 2007.

Venue
The workshop will take place at the head-quarters of ICMS, 14 India Street, Edinburgh. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.
The ICMS travel pages contain advice on how to travel to Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.

The seminar room at ICMS has whiteboards, 2 overhead projectors, a data projector and laptop.

Wireless access is available throughout the ICMS building. There are also several public PCs which may be used at any time for internet access and to check email.

Accommodation
For those who have asked ICMS to arrange accommodation, we have booked rooms in The Holiday Inn Edinburgh, which is conveniently located for the airport and is only about a 10 minute bus journey and a short walk from ICMS. For information about travel to the Holiday Inn, Corstorphine Road, Edinburgh please click here.

Alternatively, participants are free to make their own arrangements and claim back the cost, with receipts, up to a maximum of £70.00 per night bed and breakfast. A list of Edinburgh accommodation of various sorts and prices is available here. Sections 1-3 are particularly relevant.

Registration

Registration will take place between 09.00 and 09.50 on Monday 9 July, with refreshments provided. The talks will start at 10.00.

Meals and Refreshments
Morning and afternoon refreshments together with a buffet lunch will be provided throughout the workshop.

There will be an informal wine reception after the close of lectures on Monday 9 July evening.

An evening meal will be provided in a Nargile Turkish Restaurant on Tuesday 10 July. The workshop dinner will take place at First Coast Restaurant on the evening of Thursday 12 July.

On arrival you will be given a ‘welcome pack’ which contains a list of local restaurants and eating places.

Excursions

Following the talks on Wednesday 11 July, participants are invited to attend a one-hour tour at the Whisky Heritage Centre on Edinburgh's Royal Mile. Further information is available here . There is no cost to participants for this tour, which includes a whisky tasting and souvenir gift.

Financial Arrangements

Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your hotel accommodation, lunch each day, the informal wine reception and evening meals on 2 nights (see ‘Meals and Refreshments’ section above).

We wish to thank participants who have agreed to cover some or all of their own travel. For others, we are able to reimburse the travel costs estimated on your registration form and specified by email.

Reimbursement will take place after the workshop. At Registration you will be given an expenses claim form. Please note that a receipt is required for each item claimed. E-tickets for travel will be accepted if the name and amount paid is clearly shown.

Under the terms of our EPSRC funding we are required to charge a 30.00 GBP registration fee to cover costs not admissible under the grant. The fee will be payable on arrival at the workshop payment may be by cash, sterling cheque or credit/debit card.

Programme

Monday 9 July

09.00 - 09.50	Registration
09.50 - 10.00	Welcome
10.00 - 10.45	Dmitry Kramkov (Carnegie Mellon University) A model for a large investor who trades at utility indifference prices of market makers Presentation
10.45 - 11.15	Coffee/Tea
11.15 - 12.00	Huyên Pham (Université Paris 7 Diderot) Impulse control problems on finite horizon with execution delay Presentation
12.00 - 12.45	Dirk Becherer (Imperial College London) Optimal asset liquidation in illiquid markets with finite resiliency
12.45 - 14.15	Lunch
14.15 - 15.00	Chris Rogers (University of Cambridge) Illiquidity revisited Presentation
15.00 - 15.45	Mark Owen (Heriot-Watt University) Utility-based approaches to asset pricing Presentation
15.45 - 16.15	Coffee/Tea
16.15 - 17.00	Martin Schweizer (ETH Zurich) Implied volatilities (preliminary title) Presentation
17.00 - 17.45	Jan Obloj (Imperial College London) Using options to complete markets with stochastic volatility and jumps Presentation
18.00 - 19.00	Wine reception at ICMS, 14 India Street

Tuesday 10 July

09.30 - 10.15	Xin Guo (University of California, Berkeley) Connecting singular and switching controls with applications to (ir)reversible investment Presentation
10.15 - 11.00	Peter Friz (University of Cambridge) On the Black-Scholes implied volatility at extreme strike Presentation
11.00 - 11.30	Coffee/Tea
11.30 - 12.15	Mihail Zervos (London School of Economics) Itô semi-diffusion processes
12.15 - 13.00	Tim Johnson (Heriot-Watt University) The optimal timing of investment decisions Presentation
13.00 - 14.30	Lunch
14.30 - 15.15	Tomas Björk (Stockholm School of Economics) Optimal investments under partial information
15.15 - 16.00	Michael Monoyios (University of Oxford) To be confirmed Presentation
16.00 - 16.30	Coffee/Tea
16.30 - 17.15	Tom Hurd (McMaster University) Credit risk models based on time changed Brownian motion Presentation
17.15 - 18.00	Arne Lokka (King’s College London) Pricing and hedging of credit derivatives
19.00	Informal group supper at Nargile Turkish Restaurant, 73 Hanover Street

Wednesday 11 July

09.30 - 10.15	Matheus R Grasselli (McMaster University) Combining real options and games in incomplete markets Presentation
10.15 - 11.00	Michael Tehranchi (University of Cambridge) A characterisation of dynamic forward utilities Presentation
11.00 - 11.30	Coffee/Tea
11.30 - 12.15	Jan Kallsen (Technische Universität München) Mean-variance hedging for jump processes Presentation
12.15 - 13.00	Anke Wiese (Heriot-Watt University) Mean-variance hedging in stochastic volatility models driven by Lévy processes Presentation
13.00 - 14.30	Lunch
14.30 - 15.15	Andrew Lim (University of California, Berkeley) Robust decision making with relative entropy Presentation
15.15 - 16.00	Alex Cox (University of Bath) Robust hedging of options based on the local time Presentation (NB - large file)
16.00 - 16.30	Coffee/Tea
17.15 - 18.30	Optional tour of the Scotch Whisky Heritage Centre

Thursday 12 July

09.30 - 10.15	Hans Föllmer (Humboldt Universität Berlin) On the dynamics of convex risk measures
10.15 - 11.00	Giacomo Scandolo (University of Firenze) Robustness and sensitivity analysis of risk measurement procedures Presentation
11.00 - 11.30	Coffee/Tea
11.30 - 12.15	Walter Schachermayer (Technische Universität Wien) Consistent price systems and face-lifting pricing under transaction costs
12.15 - 13.00	Miklós Rásonyi (Hungarian Academy of Sciences/Vienna University of Technology) The fundamental theorem of asset pricing for continuous processes under small transaction costs
13.00 - 14.30	Lunch
14.30 - 15.15	Stefan Ankirchner (Humboldt Universität Berlin) Smoothness of indifference prices and quadratic BSDEs Presentation
15.15 - 16.00	Mihai Sîrbu (Columbia University) Asymptotic analysis of utility-based hedging strategies for small number of contingent claims
16.00 - 16.30	Coffee/Tea
16.30 - 17.15	Vicky Henderson (University of Warwick) Investment timing, incomplete markets & corporate control Presentation
19.00	Workshop Dinner at First Coast Restaurant, 99-101 Dalry Road, Edinburgh

Friday 13 July

09.30 - 10.15	Thaleia Zariphopoulou (University of Texas at Austin) Forward performance processes and their optimal allocations Presentation
10.15 - 11.00	Gordan Zitkovic (University of Texas at Austin) Market equilibria and the stability of demand Presentation
11.00 - 11.30	Coffee/Tea
11.30 - 12.15	Martijn Pistorius (King's College London) On a simple model for ruin of two insurance companies Presentation
12.15 - 13.00	Harry Zheng (Imperial College London) A counterexample of subdifferential valued optimal wealth Presentation
13.00 - 14.30	Lunch
14.30 - 15.15	David Hobson (University of Warwick) Utility maximisation, discretionary stopping and asset sales Presentation
15.15 - 15.45	Coffee/Tea

Presentations:

Presentation Details
Ankirchner, Stefan
Smoothness of indifference prices and quadratic BSDEs
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The dynamics of exponential indifference prices of contingent claims can be described as a BSDE with quadratic growth. The talk will first discuss variational and classical differentiability of such quadratic BSDEs. Then this is applied in order to express optimal hedging strategies in terms of derivatives of indifference prices with respect to the underlyings. For related papers see: http://wws.mathematik.hu-berlin.de/~ankirchn/
Becherer, Dirk
Optimal asset liquidation in illiquid markets with finite resiliency
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We discuss a new modeling approach for an illiquid financial market with finite resiliency. In this model, we study the problem, how a large trader whose orders do affect the market prices against which his orders are executed, can optimally liquidate (or acquire) a certain asset position. We obtain explicit solutions for the liquidation strategy that maximizes the liquidation proceeds. (Research project with Peter Bank, Columbia University)
Björk, Tomas
Optimal investments under partial information
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In this paper we consider optimal investment problems where the local rate of returns of the assets under consideration cannot be observed directly. The problem is that of finding the optimal portfolio strategy which maximizes the utility of terminal wealth. The constraint is that the portfolio has to be adapted to the filtration generated by observations of the asset price processes. This leads to an optimal control problem under partial information. For various special cases, problems of this kind has earlier been successfully studied by Brennan, Baeuerle, Rieder, Brendle, Nagai, Runggaldier and others. The contribution of the present paper is that we study a fairly general problem without any assumptions of a markovian structure. Within this framework we obtain surprisingly explicit formulas for optimal wealth and optimal portfolio strategies. The existing results in the literature then come out as special cases of the general theory. (Joint with Mark Davis and Camilla Landen)
Cox, Alex
Robust hedging of options based on the local time
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Quantities invloving the local time can arrive in a variety of meaningful financial situations - for example as a consequence of a stop-loss start-gain strategy, or from consideration of corridor variance swaps - and have recently been considered by Carr. In this talk, we describe a robust trading strategy in vanilla calls and the underlying, which provides a model-free bound on the price of such derivatives. (Joint work with David Hobson and Jan Obloj)
Föllmer, Hans
On the dynamics of convex risk measures
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We discuss some recent advances in the analysis of dynamic convex risk measures. In particular we characterize various notions of time-consistency in terms of corresponding supermartingale properties and explore some of their consequences, including asymptotic safety and asymptotic precision along the given filtration. This will be based on joint work with Irina Penner.
Friz, Peter
On the Black-Scholes implied volatility at extreme strike
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We discuss simple and universal formulae that give quantitative links between tail behaviour and moment explosions of the underlying on one hand, and growth of the famous volatility smile on the other hand. Practical relevance comes from model calibration and smile extrapolation from market data. The theory of regular variation provides the mathematical framework. At occasions, one can use large deviations and heat-kernel estimates.
Grasselli, Matheus R
Combining real options and games in incomplete markets
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Real options and game theory address different aspects of strategic decision-making. Using replication and arbitrage arguments, the real options approach attempts to quantify the value of time flexibility for a decision to be taken under uncertainty. On the other hand, game theory attempts to take into account the effects of competition in the decision making process, using concepts such as dominating strategies and Nash equilibrium. Evidently, any comprehensive framework for decision-making must incorporate both of these aspects, and recent literature in the subject proposes to do so by interlacing options and games into a combined pricing-decision tree. This is achieved thorough the following rules: (i) whenever a particular outcome of a game involves a wait-and-see strategy, its value is calculated as a real option and (ii) whenever the pay-off of an option at a given node involves a game, its value is calculated as the equilibrium solution to the game. However, these rules implicitly assume that the equilibrium solution to every game played along the tree can, at least in principle, be replicated by trading in a financial asset. We propose to supplement these rules with a utility-based valuation scheme to be used when such completeness assumption is not satisfied.
Guo, Xin
Connecting singular and switching controls: with applications to (ir)reversible investment
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Analysis of (ir)reversible problems from mathematical economics has evolved considerably from the initial heuristics to the more sophisticated and standard stochastic control approach. In this talk, we discuss a new theoretical connection between singular controls of finite variation and a class of switching controls. This correspondence provides a novel methodology for solving explicitly high-dimensional singular control problems, and enables us to extend the theory of (ir)reversible investment. In particular, both sufficient and necessary conditions for the well-known smooth fit principle along with the regularity of the value functions are given. And when the payoff functions satisfy the usual Inada conditions, the boundaries between action and no-action regions are smooth and strictly monotonic as postulated and exploited in the existing literature. Consequently, our result links singular controls and Dynkin games through sequential optimal stopping problems.
Henderson, Vicky
Investment timing, incomplete markets and corporate control
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This talk presents a model of investment timing by risk averse managers facing incomplete markets and corporate control. Managers are exposed to idiosyncratic risks due to the dependence of their compensation on investment payoffs which are not spanned by other assets. We show that risk averse managers invest earlier than well-diversified shareholders would prefer, leading to significant agency costs. This effect can be mitigated if the manager is subject to corporate control. Our main finding is that the interaction of incompleteness and control results in two regimes. When the market is sufficiently close to being complete, control has a strong disciplinary effect and agency costs can be virtually eliminated. However, when idiosyncratic risk is too large, shareholders suffer agency costs and control is ineffective. We solve our model in closed-form using the methodology of utility-indifference pricing and the concept of a horizon-unbiased utility function.
Hobson, David
Utility maximisation, discretionary stopping and asset sales
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In this talk we solve an optimal stopping/optimal control problem which corresponds to the decision facing a risk averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the decision over when to sell, the agent has to choose a control strategy which corresponds to a feasible wealth process. The interesting features of the solution are that it is available in a very explicit form, that for some parameter values the optimal strategy is more sophisticated than might originally be expected, and that although the set-up is based on continuous diffusions, the optimal martingale may involve a jump process. One interpretation of the solution is that it is optimal for the risk averse agent to gamble.
Hurd, Tom R
Credit risk models based on time changed Brownian motion
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Motivated by the interplay between structural and reduced form credit models, and in particular the rating class models of Jarrow, Lando and Turnbull, we propose to model the firm value process as a time changed Brownian motion. We are lead to consider modifying the classic first passage problem for stochastic processes to capitalize on this time change structure. We demonstrate that the distribution functions of such "first passage times of the second kind" are efficiently computable in a wide range of useful examples, and thus this notion of first passage can be used to define the time of default in generalized structural credit models. General formulas for credit derivatives are then proven, and shown to be easily computable. Finally, we show that by treating many firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives.
Johnson, Timothy C
The optimal timing of investment decisions
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We address the problem of the valuation of perpetual American options and then extend this to reversible investment problems. The work has been motivated by issues relating to investments in real assets, and so we accommodate a wide range of diffusions driving the value of the underlying asset as well as considering pay-offs that are not necessarily monotone, concave or smooth functions of the underlying asset's value.
Kallsen, Jan
Mean-variance hedging for jump processes
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A key problem in financial mathematics is how to hedge a contingent claim by dynamic trading in the underlying. Since models based on jump processes are incomplete, perfect replication is typically impossible. As a natural alternative one may seek to minimize the expected squared hedging error. In this talk we discuss the general structure of optimal hedging strategies as well as concrete results in specific models with stochastic volatility and jumps.
Kramkov, Dmitry
A model for a large investor who trades at utility indifference prices of market traders
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We present an equilibrium-based model for large economic agent where she trades with the market makers at their utility indifference prices. We perform an asymptotic analysis of this model for the case of "small" investor and derive as a result a liquidity correction to the prices of non-traded derivatives. The presentation is based on a joint project with Peter Bank.
Lim, Andrew
A new duality result for robust and risk-sensitive control
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The duality between robust objectives involving relative entropy, and exponential utility functions/risk-sensitive objectives, is well known. This duality has played an important role in the problem of robust decision making, and is also central in the general topic of indifference pricing as well as the theory of risk measures. In this talk I shall discuss alternative (and apparently new) representations of this duality relationship which arise in robust control problems (for example) when different components of the underlying stochastic model have different levels of model uncertainty. (For example, consider an insurance company which holds home insurance policies, which have a fairly reliable stochastic model due to the relatively stable behavior and the vast amount of historical data, as well as earthquake policies for which the risks are substantially less understood). In studying this new duality relationship, we are seeking to address the question: how should decisions and tradeoffs be made when there are different levels of model uncertainty for different sources of randomness.
Lokka, Arne
Pricing and hedging of credit derivatives
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This work in progress aims at using malliavin calculus to calculate the sensitivities of credit derivatives with respect to various parameters. This is based on the relationship between time changes of the jump times and absolutely continuous change of measures.
Monoyios, Michael
Optimal hedging under partial information
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We solve an optimal hedging problem in a basis risk model under a partial information scenario. A claim on a non-traded asset Y is hedged using a correlated traded stock S via exponential utility-based methods. This requires knowledge of the assets' expected returns, which are virtually impossible to estimate with precision, and this hampers the efficacy of the technique. We relax the assumption that agents know the asset drifts, so strategies are required to be adpated to the observation filtration generated by asset returns. This leads to a two-dimensional Kalman filtering problem whose solution incorporates Bayesian learning to counteract drift parameter uncertainty. This converts the original model to one with random drifts. We derive the marginal indifference price and hedging strategy in analytic form. This allows simulations of the residual risk process to be carried out over many asset price histories, and the resulting hedging error distribution is compared to the Black-Scholes style hedge that takes S as a perfect proxy for Y, and which does not require drift parameter estimation.
Obloj, Jan
Using options to complete markets with stochastic volatility and jumps
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The talk extends works of Romano and Touzi (1997) and Davis (2004). We consider a general stochastic volatility model with (finite variation) jumps. We show the market can be essentially always completed using a finite set of options with linearly independent payoffs. Unlike previous works, we provide a necessary and sufficient condition for market completeness. Joint work with Mark Davis and Vimal Rival.
Owen, Mark P
Utility-based approaches to asset pricing
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Utility-based approaches allow an investor to incorporate risk preferences into their perceived fair price for a financial asset. We consider two such utility-based methods. Firstly we present a dynamic theory of marginal utility-based prices. In this setting we assume the asset has zero supply and therefore should have zero demand for a representative investor. We give a characterisation of marginal utility-based price processes as a local-martingales under the optimal measure in a dual problem. Secondly we present some generalised results in the theory of utility indifference pricing, including continuity and volume asymptotics.
Pham, Huyên
Hedging and optimal investment with execution delay
Pistorius, Martijn
On a simple model for ruin of two insurance companies
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Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process we obtain a closed form expression for the ultimate ruin probability. In the general case we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cramer light-tail assumption on the claim size distribution.
Rásonyi, Miklós
The fundamental theorem of asset pricing for continuous processes under small transaction costs (joint work with P. Guasoni and W. Schachermayer)
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Consistent price systems for markets with proportional transaction costs are the natural generalizations of equivalent martingale measures in frictionless trading. We prove that for an asset price process with continuous trajectories there exist no arbitrage opportunities for arbitrarily small proportional transaction costs $varepsilon>0$ if and only if, for all varepsilon>0, there are consistent price systems under varepsilon-proportional transaction costs.
Rogers, Chris
Illiquidity revisited
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Liquidity is a major issue in the financial markets; many people talk about it, but few are willing to define it. This talk grasps the nettle, and proposes a model for liquidity which captures the essential features, yet remains sufficiently tractable that it is possible to derive the hedging strategy to be used for a European option almost as easily as for the case with no illiquidity costs.
Scandolo, Giacomo
Robustness and sensitivity analysis of risk measurement procedures
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Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a risk measure of this distribution which summarizes the risk of the portfolio. The theoretical literature on risk measures has focused on the second step, defining a risk measure as a map associating a number to a known distribution, while the estimation problem has been studied separately from the choice of the risk measure. In view of studying the interplay between these two steps, we formulate the notion of risk measurement procedure, which leads from a data set to a risk statistic and study properties of common risk measurement procedures used in financial risk management, in particular its coherence and sensitivity to a small change in the data set. Our study shows the lack of robustness of many commonly methods and reveals a conflict between subadditivity and robustness of risk measurement procedures and points to the importance of inlcuding the estimation method in the analysis of risk measures.
Schachermayer, Walter
Consistent price systems and face-lifting pricing under transaction costs
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In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class of Markovian and non-Markovian models, including geometric fractional Brownian motion. Using the constructed price systems we show under very general assumptions the following "face-lifting" result: the asymptotic superreplication price of a European contingent claim g(S_T) equals hat g(S_0), where hat g is the concave envelope of g and S_t is the price of the asset at time t. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support. (Joint work with P. Guasoni and M. Rasonyi)
Schweizer, Martin
Implied volatilities: where and why not to use them
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We give an overview of some recent results on the modelling of option price processes. The goal is to have an arbitrage-free model for the joint dynamics of an underlying and a family of options written on that, and to give sufficient conditions for proving the existence of such models which are arbitrage-free. This is joint work with Johannes Wissel (ETH Zurich).
Sîrbu, Mihai
Asymptotic analysis of utility-based hedging strategies for small number of contingent claims
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In the framework of incomplete financial models the role of hedging strategy is to provide the optimal trade-off between risk (error of replication) and return. We study the linear approximation of utility-based hedging strategies for small number of contingent claims. We show that this approximation is actually a mean-variance hedging strategy under an appropriate choice of a numeraire and a risk-neutral probability. (The presentation is based on joint work with Dmitry Kramkov)
Tehranchi, Michael
A characterization of dynamic forward utilities
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We present an explicit characterization of dynamic forward utility functions (a notion recently introduced by Musiela and Zariphopoulou) when the asset prices are continuous. This work is joint with Francois Berrier and Chris Rogers.
Wiese, Anke
Mean-variance hedging in stochastic volatility models driven by Lévy processes
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We solve the mean-variance hedging problem for stochastic volatility models driven by Levy processes assuming that the mean-variance trade-off process is depending on the volatility alone. Examples include the uncorrelated Heston model with Levy jumps and the uncorrelated Stein and Stein model with Levy jumps. We determine a candidate for the variance-optimal martingale measure and prove that it is the true variance-optimal measure. This enables us to find the variance-optimal hedging strategy and to investigate the hedging error. In a Markovian framework, the optimal strategy satisfies a three-dimensional PIDE. We illustrate our results in an insurance context.
Zariphopoulou, Thaleia
Forward performance processes and their optimal allocations
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I will introduce a new approach tp performance measurement in the context of portfolio management. The approach allows for defining optimality for all trading horizons and in non-Markovian incomplete models. I will also derive and discuss the form of the optimal policies which - despite the non-Markovian nature of the models - turn out to be stochastic feedback functionals of the controlled state. An additional property of the optimal allocations is their two fund separation, with regards to the current wealth and (subordinated) risk tolerance.
Zervos, Mihail
Itô semi-diffusion processes
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We consider a new class of continuous processes whose local evolution in time is modelled by an appropriate Ito diffusion. The increments of such a process that are associated with consecutive points in a given sequence of times provide a sequence of independent random variables, each having a prescribed distribution. This class of processes could provide an alternative to modelling asset returns by means of Levy processes that is associated with a simpler calculus as well as with market completeness.
Zheng, Harry
A counterexample of subdifferential valued optimal wealth
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We discuss utility maximization in the nonsmooth setting and give a counterexample to a conjecture made in Deelstra, Pham, and Touzi (2001) on the optimality of terminal wealth valued in an appropriate subdifferential.
Zitkovic, Gordan
Market equilibria and the stability of demand
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We investigate stability properties of the optimal-investment strategies in complete in incomplete financial markets. The obtained results can be used in the study of the problem of equilibrium pricing of non-traded contingent claims in incomplete markets. A novel fixed-point theorem for linear topological spaces which are not necessarily locally convex serves as a key ingredient in our approach.

Participants

Name	Institution
Ankirchner, Stefan	Humboldt Unversität Berlin
Bank, Peter	Columbia University
Becherer, Dirk	Imperial College London
Björk, Tomas	Stockholm School of Economics
Cairns, Andrew	Heriot-Watt University
Cox, Alex	University of Bath
Drapeau, Samuel	University of Berlin
Föllmer, Hans	Humboldt Universität Berlin
Frittelli, Marco	Università degli Studi di Milano
Friz, Peter	University of Cambridge
Grasselli, Matheus R	McMaster University
Guo, Xin	University of California, Berkeley
Henderson, Vicky	Warwick Business School
Hobson, David	University of Warwick
Hurd, Tom R	McMaster University
Johnson, Timothy C	Heriot-Watt University
Kallsen, Jan	Technische Universität München
Kramkov, Dmitry	Carnegie Mellon University
Lim, Andrew	University of California, Berkeley
Lokka, Arne	King's College London
Monoyios, Michael	University of Oxford
Obloj, Jan	Imperial College London
Owen, Mark P	Heriot-Watt University
Pham, Huyên	Université Paris 7 Diderot
Pistorius, Martijn	King's College London
Rásonyi, Miklós	Hungarian Academy of Sciences/Vienna University of Technology
Rogers, Chris	University of Cambridge
Scandolo, Giacomo	University of Firenze
Schachermayer, Walter	Vienna University of Technology
Schweizer, Martin	ETH Zurich
Sîrbu, Mihai	Columbia University
Tehranchi, Michael	University of Cambridge
Wiese, Anke	Heriot-Watt University
Zariphopoulou, Thaleia	University of Texas at Austin
Zervos, Mihail	London School of Economics
Zheng, Harry	Imperial College London
Zitkovic, Gordan	University of Texas at Austin