Insurance valuation: A computable multi-period cost-of-capital approach |
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| Institution: | 1. Université de Strasbourg & CNRS, IRMA, UMR 7501, 7 rue René Descartes, 67084 Strasbourg Cedex, France;2. Université Lyon 1, Institut de Science Financière et d’Assurances, 50 avenue Tony Garnier, 69007 Lyon, France;3. Aix Marseille Université, CNRS, EHESS, Centrale Marseille, GREQAM UMR 7316, 13002 Marseille, France;1. Netspar, CentER, Department of Econometrics and Operations Research, Tilburg University, Netherlands;2. APG and Netspar, CentER, Department of Economics, Tilburg University, Netherlands;3. Netspar, Faculty of Economics and Business, University of Amsterdam, Netherlands;1. Institute of Statistics, Biostatistics and Actuarial Science, Université Catholique de Louvain (UCL), Louvain-la-Neuve, Belgium;2. Department of Mathematics, Université Libre de Bruxelles (ULB), Bruxelles, Belgium;1. Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Science Park 107, 1098 XH Amsterdam, The Netherlands;2. Rabobank, Croeselaan 18, 3521 CB Utrecht, The Netherlands;3. CWI - National Research Institute of Applied Mathematics and Computer Science, Science Park 123, 1098 XG Amsterdam, The Netherlands;4. Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands;1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, PR China;2. Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA;3. Research Center, Shenzhen Venture Capital Group CO.LTD, Shenzhen 518048, PR China;4. School of Economics and Management, Tsinghua University, Beijing 100084, PR China;1. Department of Law, Accounting and Finance, Grenoble Ecole de Management, 12 Rue Pierre Semard, 38000 Grenoble, France;2. Department of Mathematics, Hankuk University of Foreign Studies, 81 Oedae-ro, Mohyeon-myeon, Cheoin-gu, Yongin-si, Gyeonggi-do, 449-791, Republic of Korea |
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| Abstract: | We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance. |
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| Keywords: | Valuation of insurance liabilities Multi-period valuation Market-consistent valuation Cost of capital Risk margin Dynamic risk measurement |
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