A bi-level optimization model for the asset-liability management of insurance companies

Xiaowei Chen; Qianlong Liu; Dan A. Ralescu

doi:10.3934/jimo.2022074

Article Contents

2023, Volume 19, Issue 4: 3003-3019. Doi: 10.3934/jimo.2022074

This issue Previous Article Quadratic tensor eigenvalue complementarity problems Next Article Inertial Mann-Type iterative method for solving split monotone variational inclusion problem with applications

A bi-level optimization model for the asset-liability management of insurance companies

1.
School of Finance, Nankai University, Tianjin, China
2.
Institute of Insurance and Risk Management, Department of Finance and Insurance, Lingnan University, Hong Kong, China
3.
Department of Mathematical Sciences, University of Cincinnati, United States of America

^*Corresponding author: Xiaowei Chen
^*Corresponding author: Xiaowei Chen

Received: December 2021

Revised: February 2022

Published: April 2023

The first author is supported by National Natural Science Foundation of China No. 61673225

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Abstract

Different from traditional asset-liability management where only investment allocation is considered, this paper introduces policy product allocation into asset-liability management of insurance companies. In order to balance product allocation and investment allocation, a bi-level optimization model is employed. Since the decision-making environment of the two allocation processes is full of indeterminacy, the imprecise information of the model is measured by uncertain variables in order to deal with the lack of enough historical data. To solve this bi-level Optimization problem containing uncertain variables, an uncertain bilevel programming model is used. Furthermore, we simulate a scenario to compare the bi-level optimization approach with other approaches by virtue of hybrid intelligent algorithms.

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Mathematics Subject Classification: Primary: 90B50, 91B30; Secondary: 90C70.

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Figure 1. Stackelberg Competition

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Table 1. Investment Items Parameters

Investment Items	$i$	Decision Variables	Yield rate $\xi_{i}$	Beta-Value $\beta_{i}$	Unsystematic risk $\sigma_{i}$
Risk asset 1	$1$	$A_{1}$	${\mathcal{N}}(0.1,0.01)$	$0.9$	$0.01$
Risk asset 2	$2$	$A_{2}$	${\mathcal{N}}(0.08,0.005)$	$0.6$	$ 0.005$
Risk-free asset	$3$	$A_{3}$	$0.05$	$0.5$	$0$

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Table 2. Policy Products Parameters

Policy Products	$j$	Decision Variables	Profit Margin $r_{j}$	drawing coefficient $\theta_{j}$	sale coefficient $s_{j}$
Policy 1	$1$	$P_{1}$	${\mathcal{L}}(0.1,0.12 )$	$30\%$	$1$
Policy 2	$2$	$P_{2}$	${\mathcal{L}}(0.08,0.11)$	$40\%$	$1.1$

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Table 3. Optimal Solutions of Different Programmings⁶

Approaches	Programmings	Gross Profit	Policy Allocation $\bf{P}$	Investment Allocation $\bf{A}$
Stackelberg Competition	(11)	$137.2$	$(0, 1100)$	$(162, 0,277.3)$
Decentralized Decision Making	(12), (13)	$135$	$(1000, 0)$	$(50,250, 0)$
Centralized Decision Making⁷	(14)	$134.8$	$(0, 1100)$	$(165, 0,275)$

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