Hedging claims with feedback jumps in the price process

Abstract

We study a hedging and pricing problem of a model where the price process of a risky asset has jumps with instantaneous feedback from the most recent asset price. We model these jumps with a doubly stochastic Poisson process with an intensity function depending on the current price. We find a closed form expression of the local risk minimization strategy using Fllmer and Schweizer decomposition and Feynman-Kac type integrodifferential equation. The possibility that the jumps depend on the most recent price is new for this type of model.