A short introduction to mathematical finance

Abstract

We give a brief survey of some fundamental concepts, methods and results in the mathematics of finance. The survey covers the 3 topics

Chapter 1: Markets and arbitrages.

The one-period model. The multi-period model. The continuous time model.

Chapter 2: Contingent claims and completeness.

Hedging. Complete markets.

Chapter 3: Pricing of contingent claims.

The Black and Scholes formula.