Dynamic asset-liability management problem in a continuous-time model with delay

ABSTRACT

This paper investigates a dynamic continuous-time asset-liability management (ALM) problem with delay under the mean-variance criterion. The investor allocates her wealth in a financial market consisting of one risk-free asset and one risky asset, and she is subject to a random liability. The historical information of the wealth and liability affects the investor's wealth process, which is then governed by a stochastic differential delay equation. Firstly, a general ALM problem with delay is formulated and the extended Hamilton-Jacobi-Bellman system of equations is obtained. Secondly, we focus on a linear model and derive the closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function. Meanwhile, we also derive the pre-commitment strategy for the mean-variance ALM problem with delay using the maximum principle. Finally, some numerical examples and sensitivity analysis are presented to illustrate the equilibrium investment strategies and the efficient frontiers under the equilibrium and pre-commitment frameworks.

Keywords:

• Asset-liability management
• mean-variance criterion
• time inconsistency
• stochastic differential delay equation
• Hamilton-Jacobi-Bellman equation

MSCs:

• IM52
• IE13
• IB91

Acknowledgments

The authors thank the editor and two referees for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by Major Program of National Social Science Foundation of China [grant number 18ZDA092], National Natural Science Foundation of China [grant numbers 71801186, 71771220, 71571195, 71721001], Science Foundation of Ministry of Education of China [grant number 18YJC630001], Guangdong province universities and colleges Peal River scholar funded scheme (GDUPS) (2018), Natural Science Foundation of Guangdong Province of China [grant numbers 2017A030310660, 2018A030313829], Science and Technology Planning Project of Guangdong Province [grant number 2019B101001003], and Natural Sciences and Engineering Research Council of Canada [grant number RGPIN-2016-05677].