Local Risk-Minimization for Change Point Models

Abstract

he main aim of this thesis lies in describing, as explicit as possible, the local-risk minimizing strategy for a change-point model. To this end, we analyze and investigate the mathematical structures of this model. The change-point model is a model that starts with a dynamic and switches to another dynamic immediately at some random time. This random time can represents the time of occurrence of an event that may affect the market and/or agents, such as the default of a firm, a catastrophic event, sudden adjustment of fiscal policies, etc. The most interesting feature of this random time lies in the fact that its behavior might not be seen through the public flow of information. This feature obliges us to enlarge the flow of information to include this random time. For this context, we develop the local-risk minimization and describe the optimal strategy using the public information. As applications of these results, we address the hedging problem for default sensitive contingent claims.