Partially informed investors: hedging in an incomplete market with default

Abstract

In a defaultable market, an investor trades having only partial information about the behavior of the market. Taking into account the intraday stock movements, the risky asset prices are modelled by marked point processes. Their dynamics depend on an unobservable process, representing the amount of news reaching the market. This is a marked point process, which may have common jump times with the risky asset price processes. The problem of hedging a defaultable claim is studied. In order to discuss all these topics, in this paper we examine stochastic control problems using backward stochastic differential equations (BSDEs) and filtering techniques. The goal of this paper is to construct a sequence of functions converging to the value function, each of these is the unique solution of a suitable BSDE.

Unit-linked life insurance policies: Optimal hedging in partially observable market models

“…Pricing and hedging problems for contingent claims under incomplete information using filtering techniques have been studied in credit risk context, in Frey and Runggaldier [25], Frey and Schmidt [26], Tardelli [45] and in the insurance framework in Ceci et al [17] under the hypothesis of independence between the financial and the insurance markets.…”