Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (1): 1-19.doi: 10.3969/j.issn.1005-3085.2022.01.001

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Optimal Reinsurance and Investment Strategies for Insurers with Ambiguity Aversion: Minimizing the Probability of Ruin

WANG Yuwei,   RONG Ximin,   ZHAO Hui   

  1. School of Mathematics, Tianjin University, Tianjin 300350
  • Online:2022-02-15 Published:2022-04-15
  • Supported by:
    The National Natural Science Foundation of China (11771329; 11871052).

Abstract:

The paper studies an optimal investment and reinsurance problem for an ambiguity-averse insurer (AAI) who aims to minimize the ruin probability under model ambiguity. The insurer is allowed to purchase a proportional reinsurance and invest in one risky asset. The surplus process of the insurer is described by a diffusion risk model and the price process of risky asset is described by the constant elasticity variance (CEV) model. According to the dynamic programming principle, the paper derives the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The optimal strategy and value function are obtained explicitly for special elasticity coefficients. Finally, numerical models illustrate the effects of model parameters on optimal strategy and value function. The paper finds that, the investment and reinsurance strategy of the insurer becomes more conservative when the insurer is more ambiguity averse.

Key words: ruin probability, model ambiguity, investment strategy, reinsurance strategy, HJB equation, stochastic optimal control

CLC Number: