In most practical cases, it is impossible to find an explicit expression for the distribution function of the present value of a sequence of cash flows that are discounted using some given stochastic return process. In this paper, we present an easy computable approximation for this distribution function. The approximation is a distribution function which is, in the sense of convex order, an upper bound for the original distribution function. M.J. Goovaerts and J. Dhaene would like to thank for the financial support of Onderzoeksfonds K.U.Leuven (grant OT/97/6) and F.W.O. (grant "actuarial ordering of dependent risks").Numerical results seem to indicate that the approximation is rather close in a lot of cases.

In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ−function perturbations. First, we show that results about infinitely repulsive δ−function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with δ−function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable.

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