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Optimal investment and risk control policies for an insurer: Expected utility maximization
Institution:1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. Department of Economics and International Trade, Guangdong University of Finance, Guangzhou 510521, PR China;3. School of Insurance, Central University of Finance and Economics, Beijing 100081, PR China;1. School of Finance and Statistics, East China Normal University, Shanghai, 200241, China;2. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;3. Research Center of International Finance and Risk Management, East China Normal University, Shanghai, 200241, China;1. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China;2. Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, PR China;3. School of Mathematics, Lanzhou City University, Lanzhou 730070, PR China
Abstract:Motivated by the AIG bailout case in the financial crisis of 2007–2008, we consider an insurer who wants to maximize his/her expected utility of terminal wealth by selecting optimal investment and risk control strategies. The insurer’s risk process is modeled by a jump-diffusion process and is negatively correlated with the capital gains in the financial market. We obtain explicit solutions of optimal strategies for various utility functions.
Keywords:Jump-diffusion process  Martingale approach  HARA utility  CARA utility  Quadratic utility
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