Fri, 16 Nov 2012

16:00 - 17:00
DH 1st floor SR

Efficient Discretization of Stochastic Integrals

Masaaki Fukasawa
(Osaka University)
Abstract

Abstract: Sharp asymptotic lower bounds of the expected quadratic

variation of discretization error in stochastic integration are given.

The theory relies on inequalities for the kurtosis and skewness of a

general random variable which are themselves seemingly new.

Asymptotically efficient schemes which attain the lower bounds are

constructed explicitly. The result is directly applicable to practical

hedging problem in mathematical finance; it gives an asymptotically

optimal way to choose rebalancing dates and portofolios with respect

to transaction costs. The asymptotically efficient strategies in fact

reflect the structure of transaction costs. In particular a specific

biased rebalancing scheme is shown to be superior to unbiased schemes

if transaction costs follow a convex model. The problem is discussed

also in terms of the exponential utility maximization.

Thu, 25 Oct 2012

13:00 - 14:00
DH 1st floor SR

Numerical Methods for Nash Equilibria in Multi-objective Control of Processes Governed by Partial Differential Equations

Angel Ramos
Abstract

We will discuss numerical solutions of Multi-objective Control problems governed by partial differential equations. More precisely, we will look for Nash Equilibria, which are solutions to non-cooperative differential games. First we will study the continuous case. Then, in order to compute solutions, we will combine finite difference schemes for the time discretization, finite element methods for the space discretization and a conjugate gradient algorithm (or other suitable alternative) for the iterative solution of the discrete differential game. Finally, we will apply this methodology to the solution of several test problems.

Thu, 08 Nov 2012

13:00 - 14:00
DH 1st floor SR

Economics and finance as complex systems

Doyne Farmer
Abstract

Market impact, leverage, systemic risk, and the perils of mark-to-market accounting

Market impact is the price change associated with new buy or sell orders entering the market. It provides a useful alternative to thinking in terms of supply and demand for several reasons, the most important being that there is theoretical and empirical evidence that it follows a universal law. Understanding market impact is essential for adjusting investment size, for optimizing execution tactics, and provides a useful tool for understanding market ecology and systemic risk. I will present a new method for impact-adjusted accounting, and show how it can avoid the serious problems of marking-to-market when leverage is used. Then I will discuss how market impact can be combined with network theory to understand the problem of overlapping portfolios and market crowding. Since I am a new faculty member, at the beginning of the talk I will say a bit about my interests and current projects.

Thu, 18 Oct 2012

13:00 - 14:00
DH 1st floor SR

First Year Presentations

Tigran Atoyan, Sean Ledger, Peter Spoida
Abstract

Speaker: Tigran Atoyan\\

Title: A revised approach to hedging and pricing\\

Abstract:\\

After a brief review of the classical option pricing framework, we present a motivating example on the evaluation of hedging P&L using a simplistic strategy which does very well in practice. We then present preliminary results about a relatively unknown approach called business time hedging. Some applications of the latter approach to pricing certain derivative products as well as future research directions in this topic are discussed.\\

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Speaker: Sean Ledger\\

Title: Stochastic Evolution Equations in Portfolio Credit Modelling\\

Abstract:\\

I shall present an infinite-dimension structural model for a large portfolio of credit risky assets. As the number of assets approaches infinity we obtain a limiting system with a density process. I shall outline the properties of this density process and how one can use the SPDE satisfied by this process to estimate the loss function of the portfolio. Extensions to the model shall be onsidered, including contagion effects and Lévy noise. Finally I shall present some of the numerical testing for these models.\\

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Speaker: Peter Spoida\\

Title: Robust Pricing and Hedging of the Barrier Option with a Finite Number of Intermediate Law Constraints\\

Abstract:\\

We propose a robust superhedging strategy for simple barrier options, consisting of a portfolio of calls with different maturities and a self-financing trading strategy. The superhedging strategy is derived from a pathwise inequality. We illustrate how a stochastic control ansatz can provide a good guess for finding such strategies. By constructing a worst-case model, we demonstrate that this superhedge is the cheapest possible. Our construction generalizes the Skorokhod embedding obtained by Brown, Hobson and Rogers (2001). The talk is based on joint work with Pierre Henry-Labordere, Jan Obloj and Nizar Touzi.

Fri, 02 Nov 2012

16:00 - 17:00
DH 1st floor SR

Existence and convergence of Glosten-Milgrom equilibria

Hao Xing
(London School of Economics and Political Science)
Abstract

We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the insider employs a mixed strategy to randomly submit two types of orders: one type trades in the same direction as noise trades while the other cancels some of the noise trades by submitting opposite orders when noise trades arrive. The construction also allows us to prove that Glosten-Milgrom equilibria converge weakly to Kyle-Back equilibrium, without the additional assumptions imposed in \textit{K. Back and S. Baruch, Econometrica, 72 (2004), pp. 433-465}, when the common intensity of the Poisson processes tends to infinity. This is a joint work with Umut Cetin.

Fri, 26 Oct 2012

16:00 - 17:00
DH 1st floor SR

Dawson-Watanabe superprocesses and a singular control problem arising in finance

Alexander Schied
(University of mannheim)
Abstract

We consider a class of stochastic control problems with fuel constraint that are closely connected to the problem of finding adaptive mean-variance-optimal portfolio liquidation strategies in the Almgren-Chriss framework. We give a closed-form solution to these control problems in terms of the log-Laplace transforms of certain J-functionals of Dawson-Watanabe superprocesses. This solution can be related heuristically to the superprocess solution of certain quasilinear parabolic PDEs with singular terminal condition as given by Dynkin (1992). It requires us to study in some detail the blow-up behavior of the log-Laplace functionals when approaching the singularity.

Fri, 23 Nov 2012

16:00 - 17:00
DH 1st floor SR

Exact Implied Volatility Expansions

Matt Lorig
(Princeton University)
Abstract

We derive an exact implied volatility expansion for any model whose European call price can be expanded analytically around a Black-Scholes call price. Two examples of our framework are provided (i) exponential Levy models and (ii) CEV-like models with local stochastic volatility and local stochastic jump-intensity.

Fri, 09 Nov 2012

16:00 - 17:00
DH 1st floor SR

Optimal Transport, Robust Pricing, and Trajectorial Inequalities

Mathias Beiglböck
(University of Vienna)
Abstract

Robust pricing of an exotic derivative with payoff $\Phi$ can be viewed as the task of estimating its expectation $E_Q \Phi$ with respect to a martingale measure $Q$ satisfying marginal constraints. It has proven fruitful to relate this to the theory of Monge-Kantorovich optimal transport. For instance, the duality theorem from optimal transport leads to new super-replication results. Optimality criteria from the theory of mass transport can be translated to the martingale setup and allow to characterize minimizing/maximizing models in the robust pricing problem. Moreover, the dual viewpoint provides new insights to the classical inequalities of Doob and Burkholder-Davis-Gundy.

Fri, 12 Oct 2012

16:00 - 17:00
DH 1st floor SR

Incomplete Continuous-time Securities Markets with Stochastic Income Volatility

Kasper Larsen
(Carnegie Mellon University)
Abstract

In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting equilibrium can display both lower interest rates and higher risk premia compared to the Pareto efficient equilibrium in an otherwise identical complete market. This is joint work with Peter Ove Christensen.

Fri, 02 Nov 2012

10:00 - 12:33
DH 1st floor SR

MSc project proposals

various
(Industry)
Abstract

This is the session for our industrial sponsors to propose project ideas. Academic staff are requested to attend to help shape the problem statements and to suggest suitable internal supervisors for the projects. 

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