Overview

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 … For more content click the Read More button below.

Offerings

S1-01-CLAYTON-ON-CAMPUS
S1-FF-CLAYTON-FLEXIBLE
S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Fima Klebaner

Unit Coordinator(s)

Dr Fima Klebaner
Dr Ivan Guo

Notes

IMPORTANT NOTICE:
Scheduled teaching activities and/or workload information are subject to change in response to COVID-19, please check your Unit timetable and Unit Moodle site for more details.

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Appreciate the modern approach to evaluation of uncertain future payoffs;

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

8.

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

Teaching approach

Active learning

Assessment

1 - In-semester assessment
2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions
Lectures

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous Items Required (Unit Course Reader,Printing, Stationery)- $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics