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

Kun Wu () and Weixing Wu ()
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Kun Wu: Beijing Technology and Business University
Weixing Wu: University of International Business and Economics

Journal of Quantitative Economics, 2016, vol. 14, issue 2, No 1, 167-178

Abstract: 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.

Keywords: CEV model; Proportional reinsurance; Optimal investment; Legendre transform (search for similar items in EconPapers)
JEL-codes: C60 G11 G22 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s40953-016-0032-9

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