Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Pham, Huyen^1,2,3 

[1] Univ Paris 07, CNRS, UMR 7599, Lab Probabilites & Modeles Aleatoires, F-75221 Paris 05, France

[2] Inst Univ France, Paris, France

[3] CREST ENSAE, Paris, France

关键词: Stochastic control;    Progressive enlargement of filtrations;    Decomposition in the reference filtration;    Multiple default times;    Risk management;   

DOI  :  10.1016/j.spa.2010.05.003

来源: Elsevier

【 摘 要 】

We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference filtration and the knowledge of multiple random times together with associated marks when they occur. By working under a density hypothesis on the conditional joint distribution of the random times and marks, we prove a decomposition of the original stochastic control problem under the global filtration into classical stochastic control problems under the reference filtration, which is determined in a finite backward induction. Our method revisits and extends in particular stochastic control of diffusion processes with a finite number of jumps. This study is motivated by optimization problems arising in default risk management, and we provide applications of our decomposition result for the indifference pricing of defaultable claims, and the optimal investment under bilateral counterparty risk. The solutions are expressed in terms of BSDEs involving only Brownian filtration, and remarkably without jump terms coming from the default times and marks in the global filtration. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free