Temporal Risk Processes

Abstract

This chapter provides an introduction to inter-temporal probability processes used commonly in modeling risk processes. The chapter begins with the questions “what is time,” “what is memory?” how are their definitions used to construct quantitative and temporal models. Elementary models such as probability models with the Markov property, random (binomial) walks, Poisson processes and continuous state and time stochastic processes are both presented intuitively and applied to many risk problems. These stochastic processes are then extended to more complex situations including long run memory models (fractal models), short memory models as well as to models departing from the basic Markov property and random walks models. While some of these models require a more advanced quantitative background than assumed for Chaps. 3 and 4, their applications are used to highlight both their importance and their implications to financial and risk models.