# Math 435: Mathematical Finance

## Contents

## Catalog Information

### Title

Mathematical Finance.

### (Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

### Offered

W (odd years)

### Prerequisite

One of Math 431, Stat 341, Stat 370.

### Description

The binomial asset pricing model (discrete probability). Martingales, pricing of derivative securities, random walk in financial models, random interest rates.

## Desired Learning Outcomes

The minimal expectation for this course is that students learn about mathematical finance *in the context of discrete time and finite state-spaces.* It is therefore not required that students be taught about Brownian motion, the Black-Scholes model, etc.

### Prerequisites

Students should have had an introductory course in probability.

### Minimal learning outcomes

Within the context mentioned above, students should be able to compute prices for derivative securities. They should be conversant with the standard terminology of mathematical finance and be able to use this terminology correctly in answering questions. At a minimum, students should understand the following concepts in the context of binomial decision trees:

- Martingales
- Markov processes
- Arbitrage
- Risk neutrality
- State prices
- Options
- Call and put
- American and European

- Stopping times
- Simple random walks
- Interest rate models

### Textbooks

Possible textbooks for this course include (but are not limited to):

- Steven E. Shreve,
*Stochastic Calculus for Finance I: The Binomial Asset Pricing Model*, Springer, 2005.

### Additional topics

### Courses for which this course is prerequisite

None.