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Risks 2013, 1(3), 81-100; doi:10.3390/risks1030081
Article

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

Received: 8 August 2013; in revised form: 15 October 2013 / Accepted: 17 October 2013 / Published: 25 October 2013
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
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Abstract: 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.
Keywords: forward interest rate; forward mortality rate; life insurance; stochastic diffusion process; Gaussian approximation forward interest rate; forward mortality rate; life insurance; stochastic diffusion process; Gaussian approximation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Christiansen, M.C. Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates. Risks 2013, 1, 81-100.

AMA Style

Christiansen MC. Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates. Risks. 2013; 1(3):81-100.

Chicago/Turabian Style

Christiansen, Marcus C. 2013. "Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates." Risks 1, no. 3: 81-100.

Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert