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Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method

Author

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  • Kun Wu

    (Beijing Technology and Business University
    University of International Business and Economics)

  • Weixing Wu

    (University of International Business and Economics)

Abstract

The purpose of this paper is to consider the optimal proportional reinsurance and investment strategies for an insurance company. The insurer’s surplus process is approximated by a Brownian motion with drift. The insurance company can purchase proportional reinsurance and invest the surplus in a financial market which includes one risk-free asset and one risky asset whose price is modeled by a CEV model. The primary problem is changed to the dual problem by implying Legendre transform. When the objective of the insurance company is to maximize the expected logarithmic utility from terminal wealth, the closed-form expressions for the optimal reinsurance-investment policy which is different to the Merton case to the primal optimal problem are obtained and numerical simulations are provided to demonstrate our results. Moreover, we find an interesting result that risk exposure is non-monotonic in the cost of reinsurance.

Suggested Citation

  • Kun Wu & Weixing Wu, 2016. "Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 14(2), pages 167-178, December.
    • Handle: RePEc:spr:jqecon:v:14:y:2016:i:2:d:10.1007_s40953-016-0032-9
    DOI: 10.1007/s40953-016-0032-9
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

    CEV model; Proportional reinsurance; Optimal investment; Legendre transform;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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