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Partially informed investors: hedging in an incomplete market with default

Part of: Hamilton-Jacobi theories, including dynamic programming Stochastic systems and control

Published online by Cambridge University Press:  30 March 2016

P. Tardelli
P. Tardelli*
Affiliation:
University of L'Aquila
*
∗ Postal address: Department of Industrial and Information Engineering and Economics, University of L'Aquila, 67100, Italy. Email address: [email protected]
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Abstract

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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.

Keywords

Optimal investmentexponential utilitydefault timedynamic programmingbackward stochastic differential equationfiltering

MSC classification

Primary: 49L20: Dynamic programming method
Secondary: 93E11: Filtering 93E03: Stochastic systems, general
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 718 - 735
Copyright
Copyright © 2015 by the Applied Probability Trust 

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