Optimal investment strategies for asset-liability management with affine diffusion factor processes and HARA preferences

Abstract

<p style='text-indent:20px;'>This paper investigates an optimal asset-liability management problem within the expected utility maximization framework. The general hyperbolic absolute risk aversion (HARA) utility is adopted to describe the risk preference of the asset-liability manager. The financial market comprises a risk-free asset and a risky asset. The market price of risk depends on an affine diffusion factor process, which includes, but is not limited to, the constant elasticity of variance (CEV), Stein-Stein, Schöbel and Zhu, Heston, 3/2, 4/2 models, and some non-Markovian models, as exceptional examples. The accumulative liability process is featured by a generalized drifted Brownian motion with possibly unbounded and non-Markovian drift and diffusion coefficients. Due to the sophisticated structure of HARA utility and the non-Markovian framework of the incomplete financial market, a backward stochastic differential equation (BSDE) approach is adopted. By solving a recursively coupled BSDE system, closed-form expressions for both the optimal investment strategy and optimal value function are derived. Moreover, explicit solutions to some particular cases of our model are provided. Finally, numerical examples are presented to illustrate the effect of model parameters on the optimal investment strategies in several particular cases.</p>

Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model

“…Zhang and Zhao [15] studied the optimal reinsurance-investment problem related to sparse risk based on the HARA utility function, in which the CEV model drove the price of risky assets, and they obtained the closed-form expression of the optimal strategy. Zhang [16] studied the optimal asset-liability management problem under the framework of maximizing the expected utility, taking a variety of stochastic volatility models as a particular case and using the backward stochastic differential equation (BSDE) method to derive closed-form expressions for optimal investment strategy and optimal value function. Through the research literature, it was found that the HARA utility function was more widely used than the logarithmic utility function, exponential utility function, and power utility function.…”