Risk Minimization with Incomplete Information in a Model for High-Frequency Data

We study risk-minimizing hedging-strategies for derivatives in a model where the asset price follows a marked point process with stochastic jump-intensity, which depends on some unobservable state-variable process. This model reflects stylized facts that are typical for high frequency data. We assume that agents in our model are restricted to observing past asset prices. This poses some problems for the computation of risk-minimizing hedging strategies as the current value of the state variable is unobservable for our agents. We overcome this difficulty by a two-step procedure, which is based on a projection result of Schweizer and show that in our context the computation of risk-minimizing strategies leads to a filtering problem that has received some attention in the nonlinear filtering literature. Copyright Blackwell Publishers, Inc..