de Schepper, A.; de Vylder, F.; Goovaerts, M.; Kaas, R. Interest randomness in annuities certain. (English) Zbl 0778.62098 Insur. Math. Econ. 11, No. 4, 271-281 (1992). 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) Cited in 1 ReviewCited in 16 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 60H05 Stochastic integrals Keywords:annuities certain; probability generating function; density functions; functional integration; insurance cycles; Brownian motion; Wiener process; path-integral; continuous paths PDFBibTeX XMLCite \textit{A. de Schepper} et al., Insur. Math. Econ. 11, No. 4, 271--281 (1992; Zbl 0778.62098) Full Text: DOI 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 [4] Goovaerts, M. J.; De Vylder, F.; Kaas, R., A stochastic approach to insurance cycles, Insurance: Mathematics and Economics, 11, 2, 97-107 (1992) · Zbl 0760.62095 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.