Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework

© 2020, Journal of Industrial and Management Optimization. This paper investigates the asset liability management problem for an ordinary insurance system incorporating the standard concept of proportional reinsurance coverage in a stochastic interest rate and stochastic volatility framework. The go...

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Main Authors: Zhang, Y., Wu, Yong, Wiwatanapataphee, Benchawan, Angkola, Francisca
Format: Journal Article
Language:English
Published: American Institute of Mathematical Sciences 2020
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/79263
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author Zhang, Y.
Wu, Yong
Wiwatanapataphee, Benchawan
Angkola, Francisca
author_facet Zhang, Y.
Wu, Yong
Wiwatanapataphee, Benchawan
Angkola, Francisca
author_sort Zhang, Y.
building Curtin Institutional Repository
collection Online Access
description © 2020, Journal of Industrial and Management Optimization. This paper investigates the asset liability management problem for an ordinary insurance system incorporating the standard concept of proportional reinsurance coverage in a stochastic interest rate and stochastic volatility framework. The goal of the insurer is to maximize the expectation of the constant relative risk aversion (CRRA) of the terminal value of the wealth, while the goal of the reinsurer is to maximize the expected exponential utility (CARA) of the terminal wealth held by the reinsurer. We assume that the financial market consists of risk-free assets and risky assets, and both the insurer and the reinsurer invest on one risk-free asset and one risky asset. By using the stochastic optimal control method, analytical expressions are derived for the optimal reinsurance control strategy and the optimal investment strategies for both the insurer and the reinsurer in terms of the solutions to the underlying Hamilton-Jacobi-Bellman equations and stochastic differential equations for the wealths. Subsequently, a semi-analytical method has been developed to solve the Hamilton-Jacobi-Bellman equation. Finally, we present numerical examples to illustrate the theoretical results obtained in this paper, followed by sensitivity tests to investigate the impact of reinsurance, risk aversion, and the key parameters on the optimal strategies.
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spelling curtin-20.500.11937-792632020-08-03T05:22:52Z Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework Zhang, Y. Wu, Yong Wiwatanapataphee, Benchawan Angkola, Francisca Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Asset liability management CIR stochastic interest rate model Heston stochastic volatility model insurance system with reinsurance Hamilton-Jacobi-Bellman equation stochastic optimal control TIME-CONSISTENT INVESTMENT OF-LOSS REINSURANCE OPTIMAL PORTFOLIOS STRATEGIES INSURERS MODEL CONSUMPTION CHOICE © 2020, Journal of Industrial and Management Optimization. This paper investigates the asset liability management problem for an ordinary insurance system incorporating the standard concept of proportional reinsurance coverage in a stochastic interest rate and stochastic volatility framework. The goal of the insurer is to maximize the expectation of the constant relative risk aversion (CRRA) of the terminal value of the wealth, while the goal of the reinsurer is to maximize the expected exponential utility (CARA) of the terminal wealth held by the reinsurer. We assume that the financial market consists of risk-free assets and risky assets, and both the insurer and the reinsurer invest on one risk-free asset and one risky asset. By using the stochastic optimal control method, analytical expressions are derived for the optimal reinsurance control strategy and the optimal investment strategies for both the insurer and the reinsurer in terms of the solutions to the underlying Hamilton-Jacobi-Bellman equations and stochastic differential equations for the wealths. Subsequently, a semi-analytical method has been developed to solve the Hamilton-Jacobi-Bellman equation. Finally, we present numerical examples to illustrate the theoretical results obtained in this paper, followed by sensitivity tests to investigate the impact of reinsurance, risk aversion, and the key parameters on the optimal strategies. 2020 Journal Article http://hdl.handle.net/20.500.11937/79263 10.3934/JIMO.2018141 English American Institute of Mathematical Sciences restricted
spellingShingle Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Operations Research & Management Science
Mathematics, Interdisciplinary Applications
Engineering
Mathematics
Asset liability management
CIR stochastic interest rate model
Heston stochastic volatility model
insurance system with reinsurance
Hamilton-Jacobi-Bellman equation
stochastic optimal control
TIME-CONSISTENT INVESTMENT
OF-LOSS REINSURANCE
OPTIMAL PORTFOLIOS
STRATEGIES
INSURERS
MODEL
CONSUMPTION
CHOICE
Zhang, Y.
Wu, Yong
Wiwatanapataphee, Benchawan
Angkola, Francisca
Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
title Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
title_full Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
title_fullStr Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
title_full_unstemmed Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
title_short Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
title_sort asset liability management for an ordinary insurance system with proportional reinsurance in a cir stochastic interest rate and heston stochastic volatility framework
topic Science & Technology
Technology
Physical Sciences
Engineering, Multidisciplinary
Operations Research & Management Science
Mathematics, Interdisciplinary Applications
Engineering
Mathematics
Asset liability management
CIR stochastic interest rate model
Heston stochastic volatility model
insurance system with reinsurance
Hamilton-Jacobi-Bellman equation
stochastic optimal control
TIME-CONSISTENT INVESTMENT
OF-LOSS REINSURANCE
OPTIMAL PORTFOLIOS
STRATEGIES
INSURERS
MODEL
CONSUMPTION
CHOICE
url http://hdl.handle.net/20.500.11937/79263