Finance: A Fertile Field for Applications of MC and QMC

Abstract

The finance field gives rise to complex numerical problems and the Monte Carlo method is a flexible computational tool which is ideally suited to tackle them. This paper provides a general overview of the finance discipline and discusses recent developments. In the early applications the Monte Carlo method was used to estimate prices of complex securities since these prices could be represented as multidimensional integrals. In recent years simulation methods have been used to estimate entire distributions in association with risk management applications. Simulation methods can also be used to solve optimization problems in high dimensions and we describe two notable finance applications. These axe the pricing of high dimensional American style options and the computation of optimal portfolio weights. In some circumstances low discrepancy sequences are more efficient than random numbers and we describe some new work in this area.