Optimal investment strategies for asset-liability management with affine diffusion factor processes and HARA preferences
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Optimal investment strategies for asset-liability management with affine diffusion factor processes and HARA preferences. / Zhang, Yumo.
I: Journal of Industrial and Management Optimization, Bind 19, Nr. 8, 2023, s. 5767-5796.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Optimal investment strategies for asset-liability management with affine diffusion factor processes and HARA preferences
AU - Zhang, Yumo
N1 - Publisher Copyright: © 2023, Journal of Industrial and Management Optimization.All Rights Reserved.
PY - 2023
Y1 - 2023
N2 - 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
AB - 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
KW - affine diffusion factor process
KW - Asset-liability management
KW - backward stochastic differential equation
KW - drifted Brownian motion
KW - HARA utility
U2 - 10.3934/jimo.2022194
DO - 10.3934/jimo.2022194
M3 - Journal article
AN - SCOPUS:85151885047
VL - 19
SP - 5767
EP - 5796
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
SN - 1547-5816
IS - 8
ER -
ID: 344912372