Mean–variance asset–liability management with asset correlation risk and insurance liabilities |
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| Institution: | 1. Department of Mathematics & Information Technology, Hong Kong Institute of Education, Tai Po, N.T., Hong Kong;2. Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;1. School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;2. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha, 410081, PR China;1. School of Risk and Actuarial Studies and CEPAR, UNSW Business School, The University of New South Wales, Sydney, NSW 2052, Australia;2. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China;1. School of Statistics, East China Normal University, 3663 North Zhongshan Road, Shanghai, 200062, China;2. Department of Actuarial Studies and Business Analytics, Faculty of Business and Economics, Macquarie University, NSW 2109, Australia;3. Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia;1. Department of Statistics, The Chinese University of Hong Kong, Hong Kong;2. Department of Mathematics and Information Technology, Hong Kong Institute of Education, Hong Kong |
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| Abstract: | Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved. |
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| Keywords: | Asset–liability management Correlation risk Wishart process BSDE Mean–variance criteria |
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