An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process |
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| Institution: | 1. Department of Mechanical and Industrial Engineering, 3131 Seamans Center, The University of Iowa, Iowa City, IA 52242-1527, United States;2. Department of Systems Engineering and Engineering Management, P6600, 6/F, Academic 1, City University of Hong Kong, Hong Kong;1. SMABTP Group, 114 Avenue Émile Zola, 75015, Paris, France;2. EM Lyon Business School, 23, Avenue Guy de Collongue, 69134 Ecully Cedex, France;1. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA;2. Operations Research, North Carolina State University, Raleigh, NC 27695-7913, USA;1. School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, PR China;2. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;1. Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, USA;2. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany;3. Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada;4. Polo Tecnologico IISS G. Galilei, Via Cadorna 14, 39100 Bolzano, Italy;5. Departamento de Economía Aplicada II, Facultad de Económicas, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Pozuelo, Spain |
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| Abstract: | In this paper we investigate an asset–liability management problem for a stream of liabilities written on liquid traded assets and non-traded sources of risk. We assume that the financial market consists of a risk-free asset and a risky asset which follows a geometric Lévy process. The non-tradeable factor (insurance risk or default risk) is driven by a step process with a stochastic intensity. Our framework allows us to consider financial risk, systematic and unsystematic insurance loss risk (including longevity risk), together with possible dependencies between them. An optimal investment strategy is derived by solving a quadratic optimization problem with a terminal objective and a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target. Techniques of backward stochastic differential equations and the weak property of predictable representation are applied to obtain the optimal asset allocation. |
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