11:00 - 12:00 Goran Peskir| (University of Manchester)
Optimal mean-variance selling strategies
Abstract: I will present a dynamic formulation of the mean-variance selling problem and discuss possible ways of solving it. Joint work with J L Pedersen (Copenhagen).

12:00 - 13:00 Halil Mete Soner| (ETH Zürich)
Asymptotic analysis in portfolio management
Abstract: Many of the portfolio management problems with friction do not admit explicit or traceable solutions. This makes it hard to asses the impact of friction and the design of nearly optimal strategies that are close to the frictionless ones. We propose to use asymptotic analysis to remedy this and as case studies study markets that are illiquid or ones with transaction costs. We develop an asymptotic theory using the techniques from homogenisation.

13:00 - 14:30 Lunch

14:30 - 15:30 Beatrice Acciaio| (LSE)
Arbitrage of the first kind and filtration enlargements in semimartingale financial models
Abstract: I will discuss the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition, in a general semimartingale financial model, both under initial and under progressive filtration enlargements. In both cases, I will provide a simple and general condition which is sufficient to ensure this stability for any fixed semimartingale model. Furthermore, I will give a characterization of the NA1 stability for all semimartingale models. This talk is based on a joint work with C Fontana (Évry Val-d'Essonne) and K Kardaras (LSE).

15:30 - 16:30 Mathias Beiglböck| (University of Vienna)
Model-independent finance, optimal transport and Skorokhod embedding
Abstract: Model-independent pricing has grown into an independent field in Mathematical Finance during the last 15 years. A driving inspiration in this area has been the fruitful connection to the Skorokhod embedding problem. We discuss a more recent approach to model-independent pricing, based on a link to Monge-Kantorovich optimal transport. This transport-viewpoint also sheds new light on Skorokhod's classical problem.

16:30 - 17:00 Coffee break

17:00 - 18:00 Bruno Bouchard| (University Paris Dauphine)
Stochastic target games via regularised viscosity solutions: application to super-hedging under coefficients' uncertainty
Abstract : We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic programming principle which allows us to characterize the value function as the viscosity solution of a non-linear partial differential equation. Because abstract measurable selection arguments cannot be used in this context, the main obstacle is the construction of measurable almost-optimal strategies. We propose a novel approach where smooth supersolutions are used to define almost-optimal strategies of Markovian type, similarly as in verification arguments for classical solutions of Hamilton–Jacobi–Bellman equations. The smooth supersolutions are constructed by an extension of Krylov’s method of shaken coefficients. We apply our results to a problem of option pricing under model uncertainty with different interest rates for borrowing and lending.

Day Two: Friday 25 April 2014

09:45 - 10:00 Registration

10:00 - 11:00 Philip Protter| (Columbia University)
Liquidity suppliers and high frequency trading
Abstract: We will provide a mathematical analysis of how high frequency traders profit from their speed with respect to the limit order book. Their profits can be decomposed into two components: The first is due to their ability to execute market orders at limit order prices and without incurring any liquidity costs themselves. The second is by "front running" market orders with limit prices. These trading profits are at the expense of ordinary traders who submit market orders and sophisticated traders who submit limit orders or who use algorithmic trading to split up and execute large trades.

11:00 - 11:30 Coffee break

11:30 - 12:30 Stefano De Marco| (École Polytechnique)
On the shapes of implied volatility with positive mass at zero
Abstract: We study the shapes of the implied volatility when the underlying distribution has an atom at zero. We show that the behaviour at small strikes is uniquely determined by the mass of the atom at least up to the third asymptotic order, regardless of the properties of the remaining distribution on the positive real line. We investigate the structural difference with the no-mass-at-zero case, showing how one can - a priori - distinguish between mass at the origin and a heavy-left-tailed distribution. An atom at zero is found in stochastic models with absorption at the boundary (such as CEV process), and can possibly be used to model default events (as in the class of jump-to-default models of credit risk) - we test this model-free result in such examples. On the technical side, note that while the celebrated moment formula of Lee tells that implied variance is at most asymptotically linear in log-strike, other results for exact smile asymptotics such as Benaim and Friz (09) or Gulisashvili (10) do not apply in this setting - essentially due to the breakdown of Put-Call symmetry. Joint work with C Hillairet and A Jacquier.

12:30 - 13:30 Vladimir Kaishev| (Cass Business School)
Ruin probabilities, Appell structures and related dualities
Abstract: We consider a reasonably general insurance risk model under which cumulative premium income is modelled by any non-decreasing premium income function, consecutive claims arrive according to a point process and their severities may be dependent with any joint distribution. Under some assumptions on the claim arrival (point) process, we give closed form expressions, in terms of (generalised) Appell polynomials, for some risk related quantities such as the finite-time probability of ruin and the deficit at ruin. We further provide two dual interpretations of this model, one is the so called dual risk model and the second one is a dual queuing-theoretic model. We show that the ruin probabilistic results obtained under the insurance risk model are elegantly transferred to the context of the two dual models considered, thus providing new insights into these dual areas of research

13:30 - 15:00 Lunch

15:00 - 16:00 Christoph Czichowsky| (LSE)
New phenomena in portfolio optimisation under transaction costs
Abstract: A fundamental question in portfolio optimisation under transaction costs is whether or not one can observe new effects that cannot be explained in financial markets without transaction costs. In this talk, we develop a duality framework that allows us to analyse this question and give examples that illustrate new phenomena arising in this context. This talk is based on joint work with Walter Schachermayer

16:00 - 17:00 Jaksa Cvitanic| (Caltech)
Moral hazard in dynamic risk management
Abstract: When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with respect to the risk choices of the agent. Using a recent theory of singular changes of measures for Ito processes, we formulate the principal-agent problem in this context, and solve it in the case of CARA preferences. In that case, the optimal contract is linear in these factors: the contractible sources of risk, including the output, the quadratic variation of the output and the cross-variations between the output and the contractible risk sources. Thus, path-dependent contracts naturally arise when there is moral hazard with respect to risk management. We also provide comparative statics via numerical examples.

Speakers