# American Institute of Mathematical Sciences

April  2017, 13(2): 737-755. doi: 10.3934/jimo.2016044

## Optimal reinsurance and investment strategy with two piece utility function

 1 School of Statistics, East China Normal University, Shanghai, 200241, China 2 Departments of Statistics of Actuarial Science, The University of Hong Kong, Hong Kong, China

* Corresponding author: Lv Chen

Received  November 2015 Published  August 2016

Fund Project: The first author is supported by Research Grants Council of the Hong Kong Special Administrative Region (project No. HKU 705313P), National Natural Science Foundation of China (grant number 11231005,11571113), Program of Shanghai Subject Chief Scientist (grant number 14XD1401600).

This paper studies optimal reinsurance and investment strategies that maximize expected utility of the terminal wealth for an insurer in a stochastic market. The insurer's preference is represented by a two-piece utility function which can be regarded as a generalization of traditional concave utility functions. We employ martingale approach and convex optimization method to transform the dynamic maximization problem into an equivalent static optimization problem. By solving the optimization problem, we derive explicit expressions of the optimal reinsurance and investment strategy and the optimal wealth process.

Citation: Lv Chen, Hailiang Yang. Optimal reinsurance and investment strategy with two piece utility function. Journal of Industrial & Management Optimization, 2017, 13 (2) : 737-755. doi: 10.3934/jimo.2016044
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