Risk-Sensitive Credit Portfolio Optimization under Partial Information and Contagion Risk

Abstract

This paper investigates the finite time risk-sensitive portfolio optimization in a regimeswitching credit market with physical and information-induced default contagion. The Markov regime-switching process is assumed to be unobservable, which has countable states that affect default intensities of surviving assets. The stochastic control problem is formulated under partial observations of asset prices and default events. By proving a novel martingale representation theorem based on incomplete and phasing out filtration, we characterize the value function in an equivalent form. This allows us to connect the control problem to a new type of quadratic BSDE with jumps, in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and establishing a uniform a priori estimates, we obtain the existence of a solution to this BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

Mean Field Game of Optimal Relative Investment with Jump Risk

“…To better understand the impact by systemic default risk on dynamic portfolio management, abundant recent works have considered optimal investment problems when jumps of risky assets are contagious. See, for example, Bo and Capponi (2018), Bo et al (2019a), Bo et al (2019b), Shen and Zou (2020), Bo et al (2021) among others that are based on the interacting intensity framework, allowing the credit default in one risky asset to increase the default intensities of other surviving names. See also Jin et al (2021) in the context of optimal dividend control for an insurance group.…”

Optimal dividend strategy for an insurance group with contagious default risk

“…To ensure the tractability, we work in the interacting intensity framework to model default contagion, which allows sequential defaults and assumes that the credit default of one subsidiary can affect other surviving names by increasing their default intensities. This type of default contagion has been actively studied recently in the context of portfolio management, see among [10,9,11,12,13] and many others. The key observation in these work is that the system of HJB partial differential equations (PDEs) is recursive and the depth of the recursion equals the number of risky assets.…”

Optimal Entry and Consumption under Habit Formation

“…Portfolio optimization under partial observations have been actively studied in the past decades, see a few examples among [6,7,8,22,25,34] with different financial motivations. As illustrated in these work, the value function under incomplete information filtration is strictly lower than the counterpart under full information filtration and this gap is usually regarded as the loss of information.…”