Linear and Mixed Integer Programming for Portfolio Optimization

This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples.

• Binary variables
• Financial modeling
• Integer variables
• Markowitz
• Risk management
• Transaction cost
• stochastic programming
• quantitative finance

• Department of Information Engineering, University of Brescia, Brescia, Italy

  Renata Mansini

• Institute of Control and Computation Engineering, Warsaw University of Technology, Warsaw, Poland

  Włodzimierz Ogryczak

• Department of Economics and Management, University of Brescia, Brescia, Italy

  M. Grazia Speranza

Renata Mansini is Professor of Operations Research at the Department of Information Engineering at the University of Brescia, Italy. She received her M.S. degree in Business Economics at the University of Brescia (Italy) and got her PhD in Computational Methods for Financial Decisions at the University of Bergamo (Italy) spending one year at the Olin Business School, Washington University in St. Louis (U.S.A) and working as researcher in the Center for Optimization and Semantic Control, at the System Science Department. She is author of several scientific papers most of which published in international volumes and journals such as Computers and Operations Research, Discrete Applied Mathematics, European Journal of Operational Research, IIE Transactions, INFORMS Journal on Computing, Journal of Banking & Finance, OMEGA The International Journal of Management Science, Transportation Science, Transportation Research. The main focus of her scientific activity has been on models and algorithms for complex combinatorial problems arising in different application contexts. In particular, she works on linear and mixed integer linear programming models and her interests include exact methods, heuristics, metaheuristics and hybrid algorithms for vehicle routing and arc routing problems, knapsack problems, optimization problems in procurement and in finance.

Wlodzimierz Ogryczak is Professor of Optimization & Decision Support at the Institute of Control & Computation Engineering of Warsaw University of Technology, Poland. He received both his M.Sc. and Ph.D. in Mathematics from University of Warsaw, and D.Sc. in Computer Science from Polish Academy of Sciences. He has published in many international journals including European Journal of Operational Research, Annals of Operations Research, Mathematical Programming, SIAM Journal on Optimization, Computational Optimization and Applications, OMEGA The International Journal of Management Science, IMA Journal of Management Mathematics among others. His research interests are focused on theoretical research, computer solutions and interdisciplinary applications in the area of linear and discrete optimization and decision support with the main stress on multiple criteria optimization and decision making under risk. In particular, he works on problems of equitable location, fair resource allocation, portfolio optimization, preference modeling.

M. Grazia Speranza is Professor of Operations Research at the Department of Economics and Management of the University of Brescia, Italy. She is author of more than 150 scientific papers that appeared in international volumes and journals such as Operations Research, Management Science, Computers and Operations Research, Discrete Applied Mathematics, European Journal of Operational Research, INFORMS Journal on Computing, Journal of Banking & Finance, Transportation Science, Transportation Research. Her main scientific interests include branch-and-cut and branch-and-price algorithms for mixed integer linear programming problems, heuristics and metaheuristics , combinatorial optimization, worst-case and competitive analysis, applications of mixed integer linear models to finance and to transportation and logistics. She is Associated Editor of international journals such as 4OR, International Transactions of Operations Research, Transportation Science, EURO Journal on Transportation and Logistics. She has been invited speaker and member of the scientific committee of several international conferences. She was Vice-President of IFORS (International Federation of Operational Research Societies) in 2008-09, President of EURO (Association of European Operational Research Societies) in 2011-12, President of TSL (Transportation Science and Logistics Society of INFORMS) in 2014.

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