MTH3251 Financial mathematics

When you finish this unit, you should be able to:

1. 1

   Appreciate the modern approach to evaluation of uncertain future payoffs;

2. 2

   Describe the concepts of arbitrage and fair games and their relevance to finance and insurance;

3. 3

   Understand conditional expectation, martingales, and stopping times, as well as the Optional Stopping Theorem;

4. 4

   Interpret models of random processes such as random walk, Brownian motion and diffusion, and stochastic differential equations;

5. 5

   Use Ito's formula and basic stochastic calculus to solve some stochastic differential equations;

6. 6

   Apply the Fundamental theorems of asset pricing to the Binomial and Black-Scholes models, as well as models for bonds and options on bonds;

7. 7

   Formulate discrete time Risk Model in Insurance and use the Optional Stopping Theorem to control probabilities of ruin;

8. 8

   Simulate stochastic processes and solutions of stochastic differential equations, and obtain prices by simulations.