ROBUST OPTIMAL CONTROL FOR AN INSURER WITH REINSURANCE AND INVESTMENT UNDER HESTON’S STOCHASTIC VOLATILITY MODEL BO YI † , ZHONGFEI LI ‡,§,∗ , FREDERI G. VIENS ¶ , YAN ZENG ‡ † School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China ‡ Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, China § Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China ¶ Department of Statistics, Purdue University, West Lafayette, IN 47907-2067, USA Abstract . This paper considers a robust optimal reinsurance and investment problem under He- ston’s Stochastic Volatility (SV) model for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and aims to find robust optimal strategies. The surplus process of the insurer is assumed to follow a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Heston’s SV model. By adopting the stochastic dynamic programming approach, closed-form expressions for the opti- mal strategies and the corresponding value functions are derived. Furthermore, a verification result and some technical conditions for a well-defined value function are provided. Finally, some of the model’s economic implications are analyzed by using numerical examples and sim- ulations. We find that ignoring model uncertainty leads to significant utility loss for the AAI. Moreover we propose an alternate model and associated investment strategy which would can be considered more adequate under certain finance interpretations, and which leads to significant improvements in our numerical example. Keywords: Reinsurance and investment strategy, Stochastic volatility, Robust optimal control, Utility maximization, Ambiguity-Averse Insurer. This research is supported by grants from National Natural Science Foundation of China (No. 71231008, 71201173), Humanity and Social Science Foundation of Ministry of Education of China (No. 12YJCZH267), Phi- losophy and Social Science Programming Foundation of Guangdong Province (No. GD11YYJ07) and Department of Education Social Science Foundation of Guangdong Province (No. 1213013). ∗ Corresponding author. Email address: sysumc04yb@gmail.com (Bo Yi), lnslzf@mail.sysu.edu.cn (Zhongfei Li), viens@purdue.edu (Frederi G. Viens), zengy36@mail.sysu.edu.cn (Yan Zeng). 1