Time-Consistent Investment-Reinsurance Strategies Towards Joint Interests of the Insurer and the Reinsurer Under CEV Models
Zhao, H., Weng, C., Shen, Y., Zeng, Y., (2016). Time-consistent investment-reinsurance strategies towards joint interests of the insurer and the reinsurer under CEV models. Science China Mathematics 60(2), 317-344.
28 Pages Posted: 8 May 2014 Last revised: 6 Feb 2017
Date Written: April 1, 2014
Abstract
The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework. The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly. The claim process of the insurer is governed by a Brownian motion with a drift. A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle. Both the insurer and the reinsurer are assumed to invest in a risky asset, which is distinct for each other and driven by a constant elasticity of variance model. The optimal decision is formulated on a weighted sum of the insurer's and the reinsurer's surplus processes. Upon a verification theorem, which is established with a formal proof for a more general problem, explicit solutions are obtained for the proposed investment-reinsurance model. Moreover, numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.
Keywords: Investment-reinsurance problem; Mean-variance analysis; Time-consistent strategy; Constant elasticity of variance model
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