ABSTRACT
Time-dependent evolution of risk is modeled using stochastic processes. In Chapter 5, we introduced and discussed several models for the temporal evolution of risk. Utilizing these models, it is possible to create structures that allow constructing new stochastic processes. These processes can be constructed with chosen, desired properties. The structure is developed by extending ordinary calculus to the stochastic case, by developing principles of stochastic calculus. We begin with introducing the basic construct of ordinary dierential equations for modeling a risk-free asset, and then introduce stochasticity to the model. The rest of the chapter is devoted to determining solutions to the stochastic models, by mostly focusing on simulation based analysis.
