Optimal investment under multiple defaults risk: a BSDE-decomposition approach
نویسندگان
چکیده
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.
منابع مشابه
Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach
The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of ...
متن کاملStochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management
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 decompositio...
متن کاملBsdes under Partial Information and Financial Applications
In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the Föllmer-Schweizer d...
متن کاملMultiple defaults and contagion risks
We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference defaultfree filtration in the random measure framework. On each default scenario, the formula can be interpreted as a Radon-Nikodym derivative of randommea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017