Optimal investment under multiple defaults risk: a BSDE-decomposition approach

Abstract : We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as progressive enlargement of a default-free Brownian filtration, and the dependence of default times is modelled by a conditional density hypothesis. In this Itô-jump process model, we give a decomposition of the corresponding stochastic control problem into stochastic control problems in the default-free filtration, which are determined in a backward induction. The dynamic programming method leads to a backward recursive system of quadratic Backward Stochastic Differential Equations (BSDEs) in Brownian filtration, and our main result is to prove under fairly general conditions the existence and uniqueness of a solution to this system, which characterizes explicitly the value function and optimal strategies to the optimal investment problem. We illustrate our solutions approach with some numerical tests emphasizing the impact of default intensities, loss or gain at defaults, and correlation between assets. Beyond the financial problem, our decomposition approach provides a new perspective for solving quadratic BSDEs with finite number of jumps.
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Rapport
2011
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https://hal.archives-ouvertes.fr/hal-00569230
Contributeur : Ying Jiao <>
Soumis le : jeudi 24 février 2011 - 15:27:38
Dernière modification le : jeudi 9 février 2017 - 15:03:00
Document(s) archivé(s) le : mercredi 25 mai 2011 - 03:03:57

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  • HAL Id : hal-00569230, version 1

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Ying Jiao, Idris Kharroubi, Huyen Pham. Optimal investment under multiple defaults risk: a BSDE-decomposition approach. 2011. <hal-00569230>

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