Computation of convex bounds for present value functions with random payments

In this contribution we study the distribution of the present value function of a series of random payments in a stochastic financial environment. Such distributions occur naturally in a wide range of applications within fields of insurance and finance. We obtain accurate approximations by developing upper and lower bounds in the convex-order sense for present value functions. Technically speaking, our methodology is an extension of the results of Dhaene et al. [Insur. Math. Econom. 31(1) (2002) 3–33, Insur. Math. Econom. 31(2) (2002) 133–161] to the case of scalar products of mutually independent random vectors.