**ACADEMIC YEAR 2016-17****Course** Master degree in Management

**Subject** Advanced Financial Mathematics

**Year** First

**Semester** First

**Credits** 8

**Prerequisites**

Knowledge of the basic concepts of mathematics and financial mathematics.

**Educational goals**

This course aims to give the basic quantitative tools for the analysis and solution of optimization problems, the understanding of bond markets, the selection of stock portfolios, the valuation and management of insurance coverage, and the measurement and management of risks.

**Contents**

1. Linear optimization problems, with business applications:

– Graphical solution;

– Analytical solution (system of equations and simplex method);

– Computer-based solution.

2. Portfolio Models

– Efficient portfolios with no short-sale restrictions;

– Variance-covariance matrix;

– Efficient portfolios without short sales.

3. Actuarial techniques of life and non-life insurance:

– Main contracts;

– Determination of insurance premiums;

– Mathematical and technical reserves.

**Teaching Method**

Lectures and exercises in computer lab, with an “active learning” approach.

**Reference Books**

– BENNINGA, Simon, *Financial Modeling*, 4th ed., MIT Press, April 2014.

– OLIVIERI, Annamaria, and PITACCO, Ermanno, *Introduction to Insurance Mathematics. Technical and Financial Features of Risk Transfers*, Springer, 2011.

– Notes provided by the instructor.

**Assessment Method**

Individual exam on the practical part (computer-based) and individual exam on the theoretical part.

**Criteria for Deciding on Final Paper**

– Strong attitude towards quantitative subjects.

– Merit criterion which rewards the better prepared students.

**Lectures**

**1 ^{st}**: Linear Programming (Notes provided by the instructor):

– Introduction to linear programming

– General formulation of linear programs

**2**: Linear Programming (Notes provided by the instructor):

^{nd}– Solving linear programming problems

• Graphical solution

**3**: Exercises in computer lab: Linear Programming

^{rd}**4**: Linear Programming (Notes provided by the instructor):

^{th}– Solving linear programming problems

• Analytical solution

**5**: Linear Programming (Notes provided by the instructor):

^{th}– Solving linear programming problems

• Analytical solution (system of equations)

**6**: Exercises in computer lab: Linear Programming

^{rd}**7**: Linear Programming (Notes provided by the instructor):

^{th}– Solving linear programming problems

• Analytical solution (simplex method)

**8**: Linear Programming (Notes provided by the instructor):

^{th}– Solving linear programming problems

• Analytical solution (simplex method)

**9**:Exercises in computer lab: Linear Programming

^{th}**10**: Linear Programming (Notes provided by the instructor):

^{th}– Dual linear programming problems

**11**: Exercises in computer lab: Linear Programming

^{th}**12**: Actuarial Mathematics – Introduction to Actuarial Mathematics and insurance business model (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 1):

^{th}– Life insurance Lines of business and business model

– Non-life insurance Lines of business and business model;

– Basic concepts of Probability theory

**13**: Portfolio Models – Introduction (“Financial Modeling” – Part II, Chapter 8):

^{th}– 8.1 Overview…197

– 8.2 Computing Returns for Apple and Google…197

– 8.3 Calculating Portfolio Means and Variances…202

**14**: Exercises in computer lab: Portfolio Models

^{th}**15**: Actuarial Mathematics – Non-life insurance pricing (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 9):

^{th}– Claims, premiums and equivalence principle

– Pricing and CAT risk

Exercises in computer lab: Actuarial Mathematics

**16**: Portfolio Models – Introduction (“Financial Modeling” – Part II, Chapter 8):

^{th}– 8.4 Portfolio Mean and Variance – Case of N assets…205

– 8.5 Envelope Portfolios…210

**17**: Exercises in computer lab: Portfolio Models

^{th}**18**: Actuarial Mathematics – Non-life insurance reserving (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 9)

^{th}– Non-life technical reserves

– Chain ladder approach

– Reserving risk

Exercises in computer lab: Actuarial Mathematics

**19**: Portfolio Models – Calculating Efficient Portfolios (“Financial Modeling” – Part II, Chapter 9):

^{th}– 9.1 Overview…221

– 9.2 Some Preliminary Definitions and Notation…221

– 9.3 Five Propositions on Efficient Portfolios and the CAPM…223

– 9.4 Calculating the Efficient Frontier: An Example…227

– 9.5 Finding Efficient Portfolios in One Step…234

– 9.6 Three Notes on the Optimization Procedure…236

**20**: Exercises in computer lab: Portfolio Models

^{th}**21**: Actuarial Mathematics – Life modeling and pricing (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 3):

^{th}– Biometric functions

– Mortality tables

– Discounting Cash flows

Exercises in computer lab: Actuarial Mathematics

**22-23-24**: NO LECTURES

^{th}**25**: Portfolio Models – Calculating Efficient Portfolios and the Variance-Covariance Matrix (“Financial Modeling” – Part II, Chapter 9 and 10):

^{th}– 9.7 Finding the Market Portfolio: The Capital Market Line (CML)…239

– 10.1 Overview…251

– 10.2 Computing the Sample Variance-Covariance Matrix…251

**26**: Exercises in computer lab: Portfolio Models

^{th}**27**: Actuarial Mathematics – Life insurance pricing (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 4):

^{th}– Single Premiums

– Annual Premiums

Exercises in computer lab: Actuarial Mathematics

**28**: Portfolio Models – Calculating the Variance-Covariance Matrix (“Financial Modeling” – Part II, Chapter 10):

^{th}– 10.3 The Correlation Matrix…256

– 10.4 Computing the Global Minimum Variance Portfolio (GMVP)…259

– 10.5 Four Alternatives to the Sample Variance-Covariance Matrix…261

– 10.6 Alternatives to the Sample Variance-Covariance: The Single-Index Model (SIM)…262

– 10.7 Alternatives to the Sample Variance-Covariance: Constant Correlation…264

– 10.8 Alternatives to the Sample Variance-Covariance: Shrinkage Methods…266

– 10.10 Which Method to Compute the Variance-Covariance Matrix?…271

**29**: Exercises in computer lab: Portfolio Models

^{th}**30**: Actuarial Mathematics – Life insurance reserving and value management (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 6.1 and 7.2, 7.3, 7.4):

^{th}– Life reserving

– Introduction to participating policies and Unit-Linked policies

Exercises in computer lab: Actuarial Mathematics

**31**: Portfolio Models – Efficient Portfolios Without Short Sales (“Financial Modeling” – Part II, Chapter 12):

^{th}– 12.1 Overview…291

– 12.2 A Numerical Example…292

– 12.3 The Efficient Frontier with Short-Sale Restrictions…298

– 12.5 Other Position Restrictions…302

**32**: Exercises in computer lab: Portfolio Models

^{th}**33**: Actuarial Mathematics – ERM and Economic Capital (Notes provided by the instructor & “Introduction to Insurance Mathematics” – Chapter 1):

^{th}– Solvency II balance sheet and Economic Capital

– Risk Management cycle and Risk Measures

– Capital aggregation and allocation

**34**: Portfolio Models – Exam simulation

^{th}**35**: Linear Programming – Exam simulation

^{th}**36**: Actuarial Mathematics – Exam simulation

^{th}

**ACADEMIC YEAR 2015-16****Course** Master degree in Management

**Subject** Advanced Financial Mathematics

**Year** First

**Semester** First

**Credits** 8

**Prerequisites**

Knowledge of the basic concepts of mathematics and financial mathematics.

**Educational goals**

This course aims to give the basic quantitative tools for the analysis and solution of optimization problems, the understanding of bond markets, the selection of stock portfolios, the valuation and management of insurance coverage, and the measurement and management of risks.

**Contents**

1. Linear optimization problems, with business applications:

– Graphical solution;

– Analytical solution (system of equations and simplex method);

– Computer-based solution.

2. Portfolio Models

– Efficient portfolios with no short-sale restrictions;

– Variance-covariance matrix;

– Efficient portfolios without short sales.

3. Immunization strategies:

– Duration;

– Convexity.

4. Actuarial techniques of life and non-life insurance:

– Main contracts;

– Determination of insurance premiums;

– Mathematical and technical reserves.

**Teaching Method**

Lectures and exercises in computer lab, with an “active learning” approach.

**Reference Books**

– BENNINGA, Simon, *Financial Modeling*, 4th ed., MIT Press, April 2014.

– OLIVIERI, Annamaria, and PITACCO, Ermanno, *Introduction to Insurance Mathematics. Technical and Financial Features of Risk Transfers*, Springer, 2011.

– Notes provided by the instructor.

**Assessment Method**

Individual computer-based exam and individual oral exam.

**Criteria for Deciding on Final Paper**

– Strong attitude towards quantitative subjects.

– Merit criterion which rewards the better prepared students.

**ACADEMIC YEAR 2014-15****Course** Master degree in Management

**Subject** Advanced Financial Mathematics

**Year** First

**Semester** First

**Credits** 8

**Prerequisites**

Knowledge of the basic concepts of mathematics and financial mathematics.

**Educational goals**

This course aims to give the basic quantitative tools for the analysis and solution of optimization problems, the understanding of bond markets, the selection of stock portfolios, the valuation and management of insurance coverage, and the measurement and management of risks.

**Contents**

1. Linear optimization problems, with business applications:

– Graphical solution;

– Analytical solution (system of equations and simplex method);

– Computer-based solution.

2. Portfolio Models

– Efficient portfolios with no short-sale restrictions;

– Variance-covariance matrix;

– Betas and Security Market Line;

– Efficient portfolios without short sales.

3. Actuarial techniques of life and non-life insurance:

– Main contracts;

– Determination of insurance premiums;

– Mathematical and technical reserves.

**Teaching Method**

Lectures and exercises in computer lab, with an “active learning” approach.

**Reference Books**

– BENNINGA, Simon, *Financial Modeling*, 4th ed., MIT Press, April 2014.

– OLIVIERI, Annamaria, and PITACCO, Ermanno, *Introduction to Insurance Mathematics. Technical and Financial Features of Risk Transfers*, Springer, 2011.

– Notes provided by the instructor.

**Assessment Method**

Individual computer-based exam and individual oral exam.

**Criteria for Deciding on Final Paper**

– Strong attitude towards quantitative subjects.

– Merit criterion which rewards the better prepared students.

**ACADEMIC YEAR 2013-14****Course** Master degree in Management

**Subject** Advanced Financial Mathematics

**Year** First

**Semester** First

**Credits** 8

**Prerequisites**

Knowledge of the basic concepts of mathematics and financial mathematics.

**Educational goals**

This course aims to give the basic quantitative tools for the analysis and solution of optimization problems, the understanding of bond markets, the selection of stock portfolios, the valuation and management of insurance coverage, and the measurement and management of risks.

**Contents**

1. Linear optimization problems, with business applications:

– Graphical solution;

– Analytical solution (system of equations and simplex method);

– Computer-based solution.

2. Portfolio Models

– Efficient portfolios with no short-sale restrictions;

– Variance-covariance matrix;

– Betas and Security Market Line;

– Efficient portfolios without short sales.

3. Immunization strategies:

– Duration;

– Convexity.

4. Actuarial techniques of life and non-life insurance:

– Main contracts;

– Determination of insurance premiums;

– Mathematical and technical reserves.

**Teaching Method**

Lectures and exercises in computer lab, with an “active learning” approach.

**Reference Books**

– BENNINGA, Simon, *Financial Modeling*, 4th ed., MIT Press, April 2014.

– OLIVIERI, Annamaria, and PITACCO, Ermanno, *Introduction to Insurance Mathematics. Technical and Financial Features of Risk Transfers*, Springer, 2011.

– Notes provided by the instructor.

**Assessment Method**

Individual computer-based exam and individual oral exam.

**Criteria for Deciding on Final Paper**

– Strong attitude towards quantitative subjects.

– Merit criterion which rewards the better prepared students.