Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2 
Assessment:  CW 25%, EX 75% 
Supplementary Assessment:  Likeforlike reassessment (where allowed by programme regulations) 
Requisites:  
Description:  Aims & Learning Objectives: Aims: To develop and apply the theory of probability and stochastic processes to examples from finance and economics. To facilitate an indepth 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 the exponential of a random walk; * perform simple calculations involving properties of Brownian motion; * demonstrate an indepth 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 counterexamples. 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 BlackScholes formula. 
Programme availability: 
MA50089 is Optional on the following programmes:Department of Mathematical Sciences
