Journal of Applied Probability

Partially informed investors: hedging in an incomplete market with default

P. Tardelli

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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.

Article information

Source
J. Appl. Probab., Volume 52, Number 3 (2015), 718-735.

Dates
First available in Project Euclid: 22 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1445543842

Digital Object Identifier
doi:10.1239/jap/1445543842

Mathematical Reviews number (MathSciNet)
MR3414987

Zentralblatt MATH identifier
1345.49045

Subjects
Primary: 49L20: Dynamic programming method
Secondary: 93E11: Filtering [See also 60G35] 93E03: Stochastic systems, general

Keywords
Optimal investment exponential utility default time dynamic programming backward stochastic differential equation filtering

Citation

Tardelli, P. Partially informed investors: hedging in an incomplete market with default. J. Appl. Probab. 52 (2015), no. 3, 718--735. doi:10.1239/jap/1445543842. https://projecteuclid.org/euclid.jap/1445543842


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