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Interest randomness in annuities certain. (English) Zbl 0778.62098

This paper discusses the path-integral evaluation of the expectation \[ E\left[\exp\left(-\int^ n_ 0\varphi(t,X(t))dt\right)\right], \] where \(\{X(t)\}\) is a stochastic process with continuous paths. In particular, it considers the special case \(\varphi(t,X(t))=\exp[-\delta t-X(t)]\).
Reviewer: E.Shiu (Iowa City)

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60H05 Stochastic integrals
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References:

[1] Beekman, J.A.; Fuelling, C.P., Interest and mortality randomness in some annuities, Insurance: mathematics and economics, 9, 185-196, (1990) · Zbl 0711.62100
[2] Beekman, J.A.; Fuelling, C.P., Extra randomness in certain annuity models, Insurance: mathematics and economics, 10, 275-287, (1991) · Zbl 0744.62142
[3] De Schepper, A.; Goovaerts, M.J.; Delbaen, F., The Laplace transform of annuities certain with random interest, Insurance: mathematics and economics, (1992), forthcoming · Zbl 0784.62091
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