Partially informed investors: hedging in an incomplete market with default. (English) Zbl 1345.49045

Summary: 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.


49N30 Problems with incomplete information (optimization)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
49J55 Existence of optimal solutions to problems involving randomness
49L20 Dynamic programming in optimal control and differential games
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
93E20 Optimal stochastic control
91G80 Financial applications of other theories
93E11 Filtering in stochastic control theory
93E03 Stochastic systems in control theory (general)
90C39 Dynamic programming
Full Text: DOI Euclid


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