## MATHEMATICAL FINANCE

## Syllabus

### Updated A.Y. 2022-2023

Mathematical Finance

Prof. Stefano Herzel

University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics

• Deterministic Payoffs

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Payoffs

1. Mean-Variance Portfolio Theory

2. The Capital Asset Pricing Model

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .

The bonus points will be added to the grade of the final exam.

Bonus points will be valid only until the end of the Winter exam session.

### Updated A.Y. 2022-2023

Mathematical Finance

Prof. Stefano Herzel

University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics

• Deterministic Payoffs

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Payoffs

1. Mean-Variance Portfolio Theory

2. The Capital Asset Pricing Model

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .

The bonus points will be added to the grade of the final exam.

Bonus points will be valid only until the end of the Winter exam session.

### Updated A.Y. 2021-2022

Mathematical Finance

Prof. Stefano Herzel

University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics

• Deterministic Payoffs

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Payoffs

1. Mean-Variance Portfolio Theory

2. The Capital Asset Pricing Model

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .

The bonus points will be added to the grade of the final exam.

Bonus points will be valid only until the end of the Winter exam session.

### Updated A.Y. 2021-2022

Mathematical Finance

Prof. Stefano Herzel

University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021

Course Description

• Deterministic Payoffs

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Payoffs

1. Mean-Variance Portfolio Theory

2. The Capital Asset Pricing Model

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

Bonus points will be valid only until the end of the Winter exam session.

### Updated A.Y. 2019-2020

B.S. in Business Administration and Economics University of Rome Tor Vergata

Fall 2018

Mathematical Finance

Stefano Herzel

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.

It covers the following topics:

• Deterministic Cash Flow Streams

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Cash Flows

1. Mean-Variance Portfolio Theory

2. Utility Functions and Risk Aversion

• A micro-approach to Asset Pricing

1. Investor’s preferences and prices

2. Investor’s beliefs and prices

3. Asset Pricing in incomplete Markets

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (20%) and a final exam (80%).

### Updated A.Y. 2019-2020

B.S. in Business Administration and Economics University of Rome Tor Vergata

Fall 2018

Mathematical Finance

Stefano Herzel

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.

It covers the following topics:

• Deterministic Cash Flow Streams

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Cash Flows

1. Mean-Variance Portfolio Theory

2. Utility Functions and Risk Aversion

• A micro-approach to Asset Pricing

1. Investor’s preferences and prices

2. Investor’s beliefs and prices

3. Asset Pricing in incomplete Markets

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (20%) and a final exam (80%).

### Updated A.Y. 2018-2019

B.S. in Business Administration and Economics University of Rome Tor Vergata

Fall 2018

Mathematical Finance

Stefano Herzel

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.

It covers the following topics:

• Deterministic Cash Flow Streams

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Cash Flows

1. Mean-Variance Portfolio Theory

2. Utility Functions and Risk Aversion

• A micro-approach to Asset Pricing

1. Investor’s preferences and prices

2. Investor’s beliefs and prices

3. Asset Pricing in incomplete Markets

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (20%) and a final exam (80%).

### Updated A.Y. 2018-2019

Fall 2018

Mathematical Finance

Stefano Herzel

Course Description

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.

It covers the following topics:

• Deterministic Cash Flow Streams

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

• Random Cash Flows

1. Mean-Variance Portfolio Theory

2. Utility Functions and Risk Aversion

1. Investor’s preferences and prices

2. Investor’s beliefs and prices

3. Asset Pricing in incomplete Markets

Textbook

David G. Luenberger, ”Investment Science” , Oxford University Press (2013)

Prerequisites

Basic knowledge of Mathematics and Statistics.

Evaluation

The final grade will be determined by class participation and homework (20%) and a final exam (80%).