Misspecified Filtering Theory applied to Optimal Allocation Problems in Finance

In this paper, we consider an investor who plays in a market that involves a risky asset whose instantaneous rate of return changes at unknown random times. This return rate is assumed to follow the law of a Compound Poisson Process. We construct optimal mathematical strategies in this context and we show that these strategies are based on a continuous time filter arising in Filtering Theory. We study the case where the model is misspecified and where the observations can only be made at discrete times. We give precise results that show how these misspecifications affect both the behavior of the original filter and the behavior of the traders wealth.