units

MTH3251

Faculty of Science

18 September 2017 27 July 2024

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This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

Monash University

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Andrea Collevecchio

Offered

Clayton

  • First semester 2016 (Day)

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.

Outcomes

On completion of this unit students will be able to:

  1. Appreciate the modern approach to evaluation of uncertain future payoffs;

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

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

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

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

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

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

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

Assessment

Assignments: 20%
Weekly exercises: 10%
Final examination (three hours): 70%

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

Dr Andrea Collevecchio

This unit applies to the following area(s) of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics

Prerequisites

One of MTH1030, MTH1035 or ETC2440 and one of MTH2010, MTH2015, MTH2032, MTH2222 or ETC2520. Either MTH2222 or ETC2520 is highly recommended.

Prohibitions

ETC3510, ETC5351