Optimal reinsurance-investment strategies for insurers under mean-CaR criteria

Yan Zeng; Zhongfei Li

doi:10.3934/jimo.2012.8.673

Article Contents

2012, Volume 8, Issue 3: 673-690. Doi: 10.3934/jimo.2012.8.673

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Optimal reinsurance-investment strategies for insurers under mean-CaR criteria

Yan Zeng^1, and
Zhongfei Li^2,

1.
Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275
2.
Lingnan (University) College/Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275

Received: May 31, 2011

Revised: January 31, 2012

Published: June 2012

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Abstract

This paper considers an optimal reinsurance-investment problem for an insurer, who aims to minimize the risk measured by Capital-at-Risk (CaR) with the constraint that the expected terminal wealth is not less than a predefined level. The surplus of the insurer is described by a Brownian motion with drift. The insurer can control her/his risk by purchasing proportional reinsurance, acquiring new business, and investing her/his surplus in a financial market consisting of one risk-free asset and multiple risky assets. Three mean-CaR models are constructed. By transforming these models into bilevel optimization problems, we derive the explicit expressions of the optimal deterministic rebalance reinsurance-investment strategies and the mean-CaR efficient frontiers. Sensitivity analysis of the results and a numerical example are provided.

Keywords:

Optimal proportional reinsurance-investment strategy,
insurers,
Capital-at-Risk,
Hamilton-Jacobi-Bellman equation.

Mathematics Subject Classification: Primary: 90C26; Secondary: 91B28, 49N15.

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