Introduction to Mathematical Finance and Probability for engineers

The aim of this course is to give a gentle introduction to the mathematical finance. As such the models we will consider are mainly discrete. The course is divided in three parts:

1. A short introduction to the jargon of mathematical finance. Here we use a one period model with two states and two securities to explain and illustrate the basic technical terms used in finance (target alternative, Financial Claims, Securities, Replicating portfolio…).
2. A short course in probability theory. Since we are mainly interested in discrete models, we limit ourselves to the finite probability spaces and discrete stochastic processes. Martingale theory and change of measure will be discussed.
3. The third part will be consisting of the generalization of the simple one-period model in part (1). Here we aim to treat one-period model with finite number of states and securities. We wish to study the theory of assets pricing, self-financing strategy, Black-Scholes formula for the CIR model.

I will mainly follow the book

Koch Medina, Pablo ; Merino, Sandro . Mathematical finance and probability. A discrete introduction.

Birkhäuser Verlag, Basel, 2003. x+328 pp.