Department of Mathematical Sciences, Unit Catalogue 2007/08 |
MA50089 Applied probability & finance |
| Credits: 6 |
| Level: Masters |
| Semester: 2 |
| Assessment: CW 25%, EX 75% |
| Requisites: |
|
Aims & Learning Objectives: Aims To develop and apply the theory of probability and stochastic processes to examples from finance and economics. To facilitate an in-depth understanding of the topic. Objectives: At the end of the course, students should be able to: * formulate mathematically, and then solve, dynamic programming problems; * price an option on a stock modelled by a log of a random walk; * perform simple calculations involving properties of Brownian motion; * demonstrate an in-depth understanding of the topic. Content: Dynamic programming: Markov decision processes, Bellman equation; examples including consumption/investment, bid acceptance, optimal stopping. Infinite horizon problems; discounted programming, the Howard Improvement Lemma, negative and positive programming, simple examples and counter-examples. Option pricing for random walks: Arbitrage pricing theory, prices and discounted prices as Martingales, hedging. Brownian motion: Introduction to Brownian motion, definition and simple properties.Exponential Brownian motion as the model for a stock price, the Black-Scholes formula. |