Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching

Abstract

We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize the value function, we investigate the corresponding recursive infinite-dimensional nonlinear dynamical programming equations (DPEs) based on default states. We propose to work in the following procedure: Applying the theory of monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space. The associated optimal feedback strategy is characterized by developing a rigorous verification theorem. Building upon results in the first stage, we construct a sequence of approximating risk sensitive control problems with finite states and prove that the resulting smooth value functions will converge to the classical solution of the original system of DPEs. The construction and approximation of the optimal feedback strategy for the original problem are also thoroughly discussed.AMS 2000 subject classifications: 3E20, 60J20. ∞ j=1 q ij = 0 for i ∈ Z + (i.e., j =i q ij = −q ii for i ∈ Z + ).

On the Bailout Dividend Problem for Spectrally Negative Markov Additive Models

“…The nontrivial generalization of control and optimization problems from standard single market models to models with regime-switching deserves innovative and technical treatment, which has become a vibrant research topic during the past decades. Some recent work motivated by different financial applications can be found in [5], [6], [13], [27], and [28].…”

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

“…Bielecki and Jang [15] studied an optimal allocation problem associated with defaultable bond, and their goal was to maximize the expected utility of the terminal wealth. Bo et al [16,17] considered an investment-consumption problem for an investor who can invest in a defaultable market. For more results about default risk, see , Zhu et al [19], Zhao et al [20], and Deng et al [21].…”

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

“…Risk-sensitive control approach has been an appealing criteria for portfolio selection, which incorporates the expected growth rate, the penalty term from the asymptotic variance as well as the risk sensitivity parameter into its dynamic optimization procedure. To name but a few recent work on this topic, Bielecki and Pliska (1999) identify that the risk-sensitive portfolio optimization is related to a mean-variance optimization problem; Nagai and Peng (2002) study an infinite time risk-sensitive portfolio optimization problem with an unobservable stochastic factor process; Hansen et al (2006) reformulate it as a robust criteria in which perturbations are penalized by a relative entropy; Hansen and Sargent (2007) explore a decision-making problem with hidden states and relate the prior distribution on the states to a risk-sensitive operator; Andruszkiewicz et al (2016) consider risk-sensitive asset management involving an observable regime switching process over finite states; Birge et al (2018) examine a risk-sensitive credit asset management problem with an observable stochastic factor; Bo et al (2019) recently solve a problem of risk-sensitive portfolio optimization with both default contagion and regime switching over countable states.…”