期刊
SCANDINAVIAN ACTUARIAL JOURNAL
卷 -, 期 8, 页码 725-751出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/03461238.2014.883085
关键词
stochastic optimization; mean-variance; ambiguity-averse insurer; Black-Scholes; model uncertainty
类别
资金
- NSF [DMS 0907321]
- NSFC [71231008, 71201173]
- Humanity and Social Science Foundation of Ministry of Education of China [12YJCZH267]
- National Science Foundation of Guangdong Province of China [S2013010011959]
- Philosophy and Social Science Foundation of Guangdong Province [GD11YYJ07]
- Foundation for Distinguished Young Talents in Higher Education of Guangdong of China [2012WYM-001]
In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black-Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience.
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