Risk-sensitive investment in a finite-factor model

Abstract

Abstract.A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The recently introduced approach of Klebaner and Liptser (2013) is used to prove the martingale property of the relevant density processes.

Optimal credit investment and risk control for an insurer with regime-switching

“…Figure 2 plots the optimal strategy of stocks and risk control in regime 1 at different times when the volatility of stocks varies. The default states considered here are z = (0, 1) and (1,0). A comparison between the left panel and the right panel of Figure 2 shows that the insurer decreases his/her investment in stocks and allocates a larger proportion of wealth to the liability, when the volatility of stocks increases.…”

“…Shen and Siu [18] discuss a consumption-portfolio optimization problem in a hidden Markov modulated asset price model with multiple risky assets under the situation that an economic agent only has access to information about the price processes of risky shares. Andruszkiewicz, et al [1] consider a risk-sensitive investment problem under a jump diffusion regime-switching market model. The objective of this paper is to consider an analytical framework for the portfolio allocation and risk control of an insurer, which explicitly accounts for the interaction between regime-switching and credit risk.…”

“…Since the policy space of our control problem is not assumed to be compact, the main difficulty in the analysis of solutions to this coupled system lies in the general default state and the non-Lipschitz nonlinearities of the system. Andruszkiewicz, et al [1] deal with a risk-sensitive investment problem in a finite-factor model under a compact policy space. The existence and uniqueness of solutions to their HJB equation can be established by verifying the globally Lipschitz-continuous coefficients.…”

Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching

“…Our paper aims to fill this gap and considers an interesting case when the default contagion effect can depend on regime states, possibly infinitely many. For some recent related work, it is worth noting that in the default-free market with finite regime states, Andruszkiewicz, Davis and Lleo [1] study the existence and uniqueness of the solution to the risk-sensitive asset maximization problem, and provide an ODE for the optimal value function, which may be efficiently solved numerically. Meanwhile, Das, Goswami and Rana [15] consider a risk-sensitive portfolio optimization problem with multiple stocks modeled as a multi-dimensional jump diffusion whose coefficients are modulated by an age-dependent semi-Markov process.…”

“…Second, for the finite state case, the existence and uniqueness of the solutions of the recursive DPE are analyzed based upon a backward recursion, namely from the state in which all stocks are defaulted toward the state in which all stocks are alive. It is worth noting that no bounded constraint is reinforced on the trading strategies of securities or control variables as in Andruszkiewicz, Davis and Lleo [1] and Kumar and Pal [23]. As a price to pay, the nonlinearities of the HJB dynamical systems are not globally Lipschitz continuous.…”