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Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates

Listed author(s):
  • Marcus C. Christiansen

    ()

    (Institute of Insurance Science, University of Ulm, 89069 Ulm, Germany)

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    In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 1 (2013)
    Issue (Month): 3 (October)
    Pages: 1-20

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    Handle: RePEc:gam:jrisks:v:1:y:2013:i:3:p:81-100:d:29915
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    8. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(01), pages 79-120, May.
    9. De Schepper, A. & De Vylder, F. & Goovaerts, M. & Kaas, R., 1992. "Interest randomness in annuities certain," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 271-281, December.
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