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Optimal investment for an insurer with cointegrated assets: CRRA utility

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  • Chiu, Mei Choi
  • Wong, Hoi Ying

Abstract

This paper considers the optimal investment problem for an insurer that invests in cointegrated assets subject to the random payments of insurance claims. The insurer’s objective is to maximize the expected utility of the terminal wealth subject to the cointegration dynamics of risky assets and the risk of paying out random liabilities with a compound Poisson process. We solve the continuous-time investment problems for the class of the constant relative risk averse utility function using the framework of the HJB equation. An explicit solution is derived by recognizing an exponential affine form in the derivation process. We then investigate the risk-preference of insurers toward statistical arbitrage from pairs-trading using the analytical results. Although a financial market with cointegrated risky assets implies the existence of statistical arbitrage opportunities, insurers may not be interested in those opportunities due to the social responsibility of a high level of risk aversion. However, if insurers are forced to trade cointegrated assets, the derived optimal solution enhances the investment performance.

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  • Chiu, Mei Choi & Wong, Hoi Ying, 2013. "Optimal investment for an insurer with cointegrated assets: CRRA utility," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 52-64.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:1:p:52-64
    DOI: 10.1016/j.insmatheco.2012.11.004
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    Cited by:

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    3. Wong, Tat Wing & Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Time-consistent mean–variance hedging of longevity risk: Effect of cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 56-67.
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    6. Dong-Mei Zhu & Jia-Wen Gu & Feng-Hui Yu & Tak-Kuen Siu & Wai-Ki Ching, 2021. "Optimal pairs trading with dynamic mean-variance objective," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 145-168, August.
    7. Christian Biener & Martin Eling, 2013. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 219-231, September.
    8. M. Mercè Claramunt & Maite Mármol & Xavier Varea, 2023. "Facing a Risk: To Insure or Not to Insure—An Analysis with the Constant Relative Risk Aversion Utility Function," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    9. Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Mean–variance asset–liability management with asset correlation risk and insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 300-310.
    10. Kwok, Kai Yin & Chiu, Mei Choi & Wong, Hoi Ying, 2016. "Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 353-366.
    11. Esfandi, Elaheh & Mousavi, Mir Hossein & Moshrefi, Rassam & Farhang-Moghaddam, Babak, 2020. "Insurer Optimal Asset Allocation in a Small and Closed Economy: The Case of Iran’s Social Security Organization," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 15(4), pages 445-461, October.

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