Optimal investment under multiple defaults risk: a BSDE-decomposition approach
By Ying Jiao, Idris Kharroubi, Huyen Pham. 2011
62 citations recorded by the source corpus.
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 Ito-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.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/2b6fa58253800f39cd54901a4bdd8d57c183b01b
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In Finance
In Management Science and Operations Research
Citations in the corpus
- Martingale representation property in progressively enlarged filtrations (2012, methodology): “This study is motivated by the credit risk modeling, especially by the models with multiple defaults (see [10, 22, 23]) where one needs to know the market behavior after the occurrences of the defaults to make running market activities (pricing, hedging, optimization, etc).”