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.


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