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Stochastic approximations of present value functions. (English. French, German summary) Zbl 1187.91092

Summary: The aim of this paper is to apply the method proposed by M. Denuit, C. Genest and E. Marceau [Insur. Math. Econ. 25, No. 1, 85–104 (1999; Zbl 1028.91553)] for deriving stochastic upper and lower bounds on the present value of a sequence of cash flows, where the discounting is performed under a given stochastic return process. The convex approximation provided by M. Goovaerts, J. Dhaene and A. De Schepper [“Stochastic upper bounds for present value functions”, J. Risk Insur. 67, 1–14 (2000)] and M. Goovaerts and J. Dhaene [Insur. Math. Econ. 24, No. 3, 281–290 (1999; Zbl 0942.60008)] is then compared to these stochastic bounds. On the basis of several numerical examples, it will be seen that the convex approximation seems reasonable.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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