Co-monotonicity And Upper And Lower Bounds For The Price Of Arithmetic Average Asian Put Options

In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic.Usually, we will determine approximations for sums of random variables by the theory of co-monotonicity, when the distributions of the terms are known,but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, we demonstrated the usefulness of the concept of co-monotonicity for describing dependencies between random variables in several financial and actuarial application. In addition, using the theory of co-monotonicity, we have given the application in a Black & Scholes setting, and also derived lower bounds and upper bounds for the price of arithmetic Asian put options.