Efficient approximations for numbers of survivors in the Lee–Carter model |
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| Institution: | 1. Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona), Spain;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain;3. Department of Econometrics, University of Barcelona, Diagonal 690, 08034 Barcelona, Spain;4. CWI – Centrum Wiskunde & Informatica, NL-1090 GB Amsterdam, The Netherlands;5. Delft University of Technology, Delft Institute of Applied Mathematics, 2628 CD Delft, The Netherlands;1. Institute of Finance and Development, Nankai University, Tianjin 300071, China;2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;3. School of Business, Nankai University, Tianjin 300071, China |
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| Abstract: | In portfolios of life annuity contracts, the payments made by an annuity provider (an insurance company or a pension fund) are driven by the random number of survivors. This paper aims to provide accurate approximations for the present value of the payments made by the annuity provider. These approximations account not only for systematic longevity risk but also for the diversifiable fluctuations around the unknown life table. They provide the practitioner with a useful tool avoiding the problem of simulations within simulations in, for instance, Solvency 2 calculations, valid whatever the size of the portfolio. |
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| Keywords: | Life annuity Mortality projection Lee–Carter model Comonotonicity Supermodular order Increasing directionally convex order Risk measures |
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