Department of Mathematical Sciences, Unit Catalogue 2008/09 |
MA30089 Applied probability & finance |
Credits: 6 |
Level: Honours |
Semester: 2 |
Assessment: EX 100% |
Requisites: |
Before taking this unit you must take MA20036 |
Aims & Learning Objectives: Aims: To develop and apply the theory of probability and stochastic processes to examples from finance and economics. 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. 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. |