Events Calendar

Jump-Diffusion Risk-Sensitive Asset Management

Math Finance Colloquium and Probability/Statistics Seminar "Jump-Diffusion Risk-Sensitive Asset Management"Prof. Mark H.A Davis, Imperial College LondonThis paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps.The main result of the paper is that the Hamilton-Jacobi-Bellman equation for this problem has a classical solution. The proof uses Bellman's "policy improvement" method together with results on linear parabolic PDEs due to Ladyzhenskaya et al. This is joint work with Sebastien Lleo.BIO: Mark Davis is currently a Professor of Mathematics at Imperial College London, specializing in stochastic analysis and financial mathematics, in particular in credit risk models, pricing in incomplete markets and stochastic volatility. He also acts as a consultant to Hanover Square Capital Partners, a newly-founded capital markets company. From
1995-1999 he was Head of Research and Product Development at Tokyo-Mitsubishi International, leading a front-office group providing pricing models and risk analysis for fixed-income, equity and credit-related products. Prof. Davis holds a PhD from the University of California Berkeley and is the author of three books on stochastic analysis and optimization. He was a founding co-editor of the journal Mathematical Finance (1990-93) and is currently an associate editor of Quantitative Finance. He was awarded the Naylor Prize in Applied Mathematics by the London Mathematical Society in 2002.FRIDAY, November 20, 2009, 3:30-4:30 PM, KAPRIELIAN HALL ROOM 414

Location: Kaprielian Hall (KAP) - 414

Audiences: Everyone Is Invited

Contact: Georgia Lum