units

MTH3251

Faculty of Science

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Monash University Handbook 2010 Undergraduate - Unit

6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

LevelUndergraduate
FacultyFaculty of Science
OfferedClayton First semester 2010 (Day)
Coordinator(s)Professor Fima Klebaner

Synopsis

Random variables, application to models of random payoffs. Conditional expectation. Normal distribution and multivariate normal distribution. Best predictors. Stochastic (random) processes. Random walk. Limit theorems. Brownian motion. Ito integral and Ito's formula. Black-Scholes, Ornstein-Uhlenbeck process and Vasicek's stochastic differential equations. Martingales. Gambler's ruin. Fundamental theorems of Mathematical Finance. Binomial and Black-Scholes models. Models for Interest Rates. Risk models in insurance. Ruin probability bound. Principles of simulation. Use of Excel package.

Objectives

On the completion of this unit students will gain an understanding of the methods of modern probability and random processes, and develop skills for modelling of random systems. Students will be able to apply this knowledge and skills in the context of financial and insurance modelling.

Assessment

Assignments: 30%
Final examination (three hours): 70%

Chief examiner(s)

Professor Fima Klebaner

Contact hours

Three 1-hour lectures and one 1-hour support class per week

Prerequisites

MTH1030 and one of MTH2032 or MTH2010

Prohibitions

ETC3510, ETC3514