DH 1st floor SR

In this work, we consider the hedging error due to discrete trading in models with jumps. We propose a framework enabling to

(asymptotically) optimize the discretization times. More precisely, a strategy is said to be optimal if for a given cost function, no strategy has

(asymptotically) a lower mean square error for a smaller cost. We focus on strategies based on hitting times and give explicit expressions for

the optimal strategies. This is joint work with Peter Tankov.

In the SABR model of Hagan et al. [2002] a perturbative expansion approach yields a tractable approximation to the implied volatility smile. This approximation formula has been adopted across the financial markets as a means of interpolating market volatility surfaces. All too frequently - in stressed markets, in the long-dated FX regime - the limitations of this approximation are pronounced. In this talk a highly efficient conditional integration approach, motivated by the work of Stein and Stein [1991] and Willard [1997], will be presented that when applied to the SABR model not only produces a volatility smile consistent with the underlying SABR process but gives access to the joint distribution of the asset and its volatility. The latter is particularly important in understanding the dynamics of the volatility smile as it evolves through time and the subsequent effect on the pricing of exotic options.

William McGhee is Head of Hybrid Quantitative Analytics at The Royal Bank of Scotland and will also discuss within the context of this presentation the interplay of mathematical modelling and the technology infrastructure required to run a complex hybrids trading business and the benefits of highly efficient numerical algorithms."

In this paper we deal with the utility maximization problem with a

preference functional of expected utility type. We derive a new approach

in which we reduce the utility maximization problem with general utility

to the study of a fully-coupled Forward-Backward Stochastic Differential

Equation (FBSDE).

The talk is based on joint work with Ying Hu, Peter Imkeller, Anthony

Reveillac and Jianing Zhang.

The standard approach to continuous-time finance starts from postulating a

statistical model for the prices of securities (such as the Black-Scholes

model). Since such models are often difficult to justify, it is

interesting to explore what can be done without any stochastic

assumptions. There are quite a few results of this kind (starting from

Cover 1991 and Hobson 1998), but in this talk I will discuss

probability-type properties emerging without a statistical model. I will

only consider the simplest case of one security, and instead of stochastic

assumptions will make some analytic assumptions. If the price path is

known to be cadlag without huge jumps, its quadratic variation exists

unless a predefined trading strategy earns infinite capital without

risking more than one monetary unit. This makes it possible to apply the

known results of Ito calculus without probability (Follmer 1981, Norvaisa)

in the context of idealized financial markets. If, moreover, the price

path is known to be continuous, it becomes Brownian motion when physical

time is replaced by quadratic variation; this is a probability-free

version of the Dubins-Schwarz theorem.

Abstract: In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in \cite{CO} to the situation where the agent is initially endowed with a random and possibly unbounded quantity of assets. We start by studying some basic properties of the value function (which is now defined on a space of random variables), then we dualize the problem following some convex analysis techniques which have proven very useful in this field of research. We finally prove the existence of a solution to the dual and (under an additional boundedness assumption on the endowment) to the primal problem. The last section of the paper is devoted to an application of our results to utility indifference pricing. This is a joint work with G. Benedetti (CREST).

Please note that this is taking place in the afternoon - partly to avoid a clash with the OCCAM group meeting in the morning.

The following two topics are likely to be discussed.

A) Modelling the collective behaviour of chicken flocks. Marian Dawkins has a joint project with Steve Roberts in Engineering studying the patterns of optical flow in large flocks of commercial broiler chickens. They have found that various measurements of flow (such as skew and kurtosis) are predictive of future mortality. Marian would be interested in seeing whether we can model these effects.
B) Asymmetrical prisoners’ dilemma games. Despite massive theoretical interest, there are very few (if any) actual examples of animals showing the predicted behaviour of reciprocity with delayed reward. Marian Dawkins suspects that the reason for this is that the assumptions made are unrealistic and she would like to explore some ideas about this.

Please note the slightly early start to accommodate the OCCAM group meeting that follows.

10am Radius Health - Mark Evans

10:30am NAG - Mick Pont and Lawrence Mulholland

Please note, that Thales are also proposing several projects but the academic supervisors have already been allocated.