An Introduction to Matrix Variate Stochastics

Abstract

So far in this book, scalar-and vector valued processes have been discussed. Chapter 10 sets the scene for matrix-valued processes. It is a stand-alone, self-contained chapter, which introduces matrix variate stochastics in a comprehensive manner: first, matrix-valued random variables are defined, then matrix-valued stochastic processes, and finally matrix-valued stochastic differential equations. To illustrate the theory developed in this chapter, we apply it to concrete examples: firstly, we discuss the matrix-valued version of the Ornstein-Uhlensteck process, whose scalar- and vector-valued versions we had already discussed in Chap. 2. Finally, we revisit the Minimal Market Model from Chap. 3, this time employing matrix-valued stochastic processes.