Soren S Nielson & Andrea Consiglio 
Practical Financial Optimization 
A Library of GAMS Models

In Practical Financial Optimization: A Library of GAMS
Models, the authors provide a diverse set of models for
portfolio optimization, based on the General Algebraic Modelling
System. ‘GAMS’ consists of a language which allows a
high-level, algebraic representation of mathematical models and a
set of solvers – numerical algorithms – to solve them.
The system was developed in response to the need for powerful and
flexible front-end tools to manage large, real-life models.

The work begins with an overview of the structure of the GAMS
language, and discusses issues relating to the management of data
in GAMS models. The authors provide models for mean-variance
portfolio optimization which address the question of trading off
the portfolio expected return against its risk. Fixed income
portfolio optimization models perform standard calculations and
allow the user to bootstrap a yield curve from bond prices.
Dedication models allow for standard portfolio dedication with
borrowing and re-investment decisions, and are extended to deal
with maximisation of horizon return and to incorporate various
practical considerations on the portfolio tradeability.
Immunization models provide for the factor immunization of
portfolios of treasury and corporate bonds.

The scenario-based portfolio optimization problem is addressed
with mean absolute deviation models, tracking models, regret
models, conditional Va R models, expected utility maximization
models and put/call efficient frontier models. The authors employ
stochastic programming for dynamic portfolio optimization,
developing stochastic dedication models as stochastic extensions of
the fixed income models discussed in chapter 4. Two-stage and
multi-stage stochastic programs extend the scenario models analysed
in Chapter 5 to allow dynamic rebalancing of portfolios as time
evolves and new information becomes known. Models for structuring
index funds and hedging interest rate risk on international
portfolios are also provided.

The final chapter provides a set of ‘case studies’:
models for large-scale applications of portfolio optimization,
which can be used as the basis for the development of business
support systems to suit any special requirements, including models
for the management of participating insurance policies and personal
asset allocation.

The title will be a valuable guide for quantitative developers
and analysts, portfolio and asset managers, investment strategists
and advanced students of finance.

Table of Content

Preface.

Acknowledgments.

Notation.

List of Models.

1 An Introduction to the GAMS Modeling System.

1.1 Preview.

1.2 Basics of Modeling.

1.3 The GAMS Language.

1.4 Getting Started.

Notes and References.

2 Data Management.

2.1 Preview.

2.2 Basics of Data Handling.

2.3 Data Generation.

2.4 A Complete Example: Portfolio Dedication.

3 Mean-Variance Portfolio Optimization.

3.1 Preview.

3.2 Basics of Mean-Variance Models.

3.3 Sharpe Ratio Model.

3.4 Diversification Limits and Transaction Costs.

3.5 International Portfolio Management.

4 Portfolio Models for Fixed Income.

4.1 Preview.

4.2 Basics of Fixed-Income Modeling.

4.3 Dedication Models.

4.4 Immunization Models.

4.5 Factor Immunization Model.

4.6 Factor Immunization for Corporate Bonds.

5 Scenario Optimization.

5.1 Preview.

5.2 Data sets.

5.3 Mean Absolute Deviation Models.

5.4 Regret Models.

5.5 Conditional Value-at-Risk Models.

5.6 Utility Maximization Models.

5.7 Put/Call Efficient Frontier Models.

6 Dynamic Portfolio Optimization with Stochastic
Programming.

6.1 Preview.

6.2 Dynamic Optimization for Fixed-Income Securities.

6.3 Formulating Two-Stage Stochastic Programs.

6.4 Single Premium Deferred Annuities: A Multi-stage Stochastic
Program.

7 Index Funds.

7.1 Preview.

7.2 Models for Index Funds.

8 Case Studies in Financial Optimization.

8.1 Preview.

8.2 Application I: International Asset Allocation.

8.3 Application II: Corporate Bond Portfolio Management.

8.4 Application III: Insurance Policies with Guarantees.

8.5 Application IV: Personal Financial Planning.

Bibliography.

Index.

About the author

ANDREA CONSIGLIO is professor of Mathematical Finance at the
University of Palermo, Italy. He has held positions at the
University of Calabria and at the University of Cyprus. He has
participated in consultancy projects with the Banca della Svizzera
Italiana, Switzerland and Prometeia, Italy. He has co-authored one
book and numerous articles for various leading academic journals.
In 2006 he was awarded the EURO Excellence in Practice Award,
jointly with Stavros A. Zenios and Flavio Cocco. His research
interests encompass many areas in the field of financial modeling
and computational finance. He holds a Ph D in applied mathematics to
finance and economics.

SØREN NIELSEN (1959-2003) was an Associate Professor
in the Department of Informatics and Mathematical Modeling at the
Technical University of Denmark. He worked at the World Bank and
the University of Texas at Austin. He held degrees in computer
science and a Ph D in decision sciences from the Wharton School of
the University of Pennsylvania.

STAVROS A. ZENIOS is Professor of Finance and Management
Science at the University of Cyprus, Director of the HERMES
European Centre of Excellence on Computational Finance and
Economics, and Senior Fellow at the Wharton Financial Institutions
Centre of the University of Pennsylvania. He has co-authored more
than 130 articles in some of the premier journals in the filed,
serves on the editorial board of six journals, and received
numerous awards for his research and publications. His previous
books include Practical Financial Optimization: Decision Making
for Financial Engineers (Blackwell Publishing, 2007);
Performance of Financial Institutions: Efficiency, Innovation,
Regulation (Cambridge University Press, 2000); Parallel
Optimization: Theory, Algorithms, and Applications (Oxford
University Press, 1997); and Financial Optimization
(Cambridge University Press, 1996).