Application of Stochastic Control to Pricing and Hedging in Lèvy Markets
Stochastic processes with discontinuous paths are being increasingly considered as relevant alternatives to the log-normal Black-Scholes model. This talk addresses the question of pricing and hedging derivatives in markets driven by Lèvy processes. These markets are incomplete and one possible approach is based on indifference pricing, as introduced by Hodges and Neuberger. This leads to utility maximization problems which can be studied by using the methods of stochastic control for jump diffusions, including the theory of viscosity solutions for Hamilton-Jacobi-Bellman partial integro-differential equations. We shall derive and analyze these equations via dynamic programming and provide numerical experiments for Lèvy processes and exponential utility functions.
(Joint work with Peter Tankov, Universitè Paris VII)
Agnès Sulem, INRIA