Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

Lihua Bian; Zhongfei Li; Haixiang Yao

doi:10.3934/jimo.2020026

Article Contents

2021, Volume 17, Issue 3: 1383-1410. Doi: 10.3934/jimo.2020026

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Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

1.
School of Finance and Economics, Qinghai University, Xining 810016, PR China
2.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China
3.
Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China
4.
School of Management, Xinhua College of Sun Yat-sen University, Guangzhou 510520, China
5.
School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China

^* Corresponding author: Zhongfei Li
^* Corresponding author: Zhongfei Li

Received: November 30, 2018

Revised: September 30, 2019

Early access: February 2020

Published: May 2021

This research is supported by the National Natural Science Foundation of China (Nos. 71721001, 71871071, 71471045), the Natural Science Foundation of Guangdong Province of China (Nos. 2014A030312003, 2017A030313399, 2018B030311004), the Innovation Team Project of Guangdong Colleges and Universities (No. 2016WCXTD012), and the Innovative School Project in Higher Education of Guangdong Province of China (No. GWTP-GC-2017-03)

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Abstract

In this paper, we investigate a multi-period mean-variance asset-liability management problem with stochastic interest rate and seek its time-consistent strategy. The financial market is assumed to be composed of one risk-free asset and multiple risky assets, and the stochastic interest rate is characterized by the discrete-time Vasicek model proposed by Yao et al. (2016a)[38]. We regard this problem as a non-cooperative game whose equilibrium strategy is the desired time-consistent strategy. We derive the analytical expressions of the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier by the extended Bellman equation. Some special cases of our model are discussed, and some properties of our equilibrium strategy, including a two-fund separation theorem, are proposed. Finally, a numerical example with real data is given to illustrate our theoretical results.

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Mathematics Subject Classification: Primary: 91G10, 93C55; Secondary: 93E20.

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Figure 1. The equilibrium strategies with and without liability

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Figure 2. The surplus process of the equilibrium strategies with and without liability

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Figure 3. The effect of liability on the equilibrium strategy

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Figure 4. The effect of stochastic interest rate on the equilibrium strategy

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Figure 5. A comparison of the equilibrium strategy and precommitment strategy

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Figure 6. The effect of liability on the equilibrium efficient frontier

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Figure 7. The effect of stochastic interest rate on the equilibrium efficient frontier

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Figure 8. A comparison of the equilibrium efficient frontier and pre-commitment efficient frontier

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