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

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    Authors
    Zhang, Y.
    Wu, Yong
    Wiwatanapataphee, Benchawan
    Angkola, Francisca
    Date
    2020
    Type
    Journal Article
    
    Metadata
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    Citation
    Zhang, Y. and Wu, Y. and Wiwatanapataphee, B. and Angkola, F. 2020. Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework. Journal of Industrial and Management Optimization. 16 (1): pp. 71-101.
    Source Title
    Journal of Industrial and Management Optimization
    DOI
    10.3934/JIMO.2018141
    Faculty
    Faculty of Science and Engineering
    School
    School of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/79263
    Collection
    • Curtin Research Publications
    Abstract

    © 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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