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.
Document type :
Reports
2011
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00569230
Contributor : Ying Jiao <>
Submitted on : Thursday, February 24, 2011 - 3:27:38 PM
Last modification on : Thursday, February 9, 2017 - 3:03:00 PM
Document(s) archivé(s) le : Wednesday, May 25, 2011 - 3:03:57 AM

Files

JKP-BSDE.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00569230, version 1

Collections

Citation

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

Share

Metrics

Record views

385

Document downloads

189