Chapter 24 Large Deviation Techniques and Financial Applications

This chapter introduces large deviation techniques and surveys recent applications in finance. Large deviations deal with the theory of rare events and can be used to establish exponential bounds on the probability of such events. If we can establish a so-called large deviation principle for a family of random variables this provides information not only on convergence but also on the speed of convergence. We begin with an introduction to large deviations and outline some of the major results. We discuss a number of applications in finance. These include applications in portfolio management, risk management and Monte Carlo simulations. We also describe some recent work which uses concepts from large deviations to analyze incomplete markets and we illustrate this application with stochastic volatility models.