Stochastic control, default risk and liquidity risk

Abstract : This PhD dissertation consists of three independent parts and deals with applications of stochastic control to finance. In the first part, we study the utility maximization problem in a market with defaults and total/partial information. The dynamic programming principle is used to characterize the value function. Given this characterization, we find a BSDE of which the value function is a solution. We also give an approximation of this value function. In the second part, we study BSDEs with jumps. We link BSDEs with jumps and Brownian BSDEs using the decomposition of processes in the reference filtration. With this link, we get a result of existence, a comparison theorem and a decomposition of Feynman-Kac formula. We use these techniques to work out the price of a European option in a complete market and the indifference price of a contingent claim in an incomplete market. Finally, in the third part, we use the error theory to explain the liquidity risk and to model the Bid-Ask spread. Then we solve an optimal liquidation problem for a large portfolio in discrete and deterministic time.
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https://tel.archives-ouvertes.fr/tel-00499532
Contributor : Thomas Lim <>
Submitted on : Friday, July 9, 2010 - 6:52:44 PM
Last modification on : Tuesday, May 14, 2019 - 11:02:21 AM
Long-term archiving on : Tuesday, October 23, 2012 - 10:10:51 AM

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  • HAL Id : tel-00499532, version 1

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T. Lim. Stochastic control, default risk and liquidity risk. Mathematics [math]. Université Paris-Diderot - Paris VII, 2010. English. ⟨tel-00499532⟩

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