Benchmark Tracking Portfolio Problems with Stochastic Ordering Constraints

The book “Benchmark Tracking Portfolio Problems with Stochastic Ordering Constraints” analyzes the problem of optimizing the portfolio composition according to specific management styles. In particular, three main tracking strategies can be identify: passive, enhanced indexing and active. This essay addresses these problems proposing theoretical and methodological solution to maximize investors' preferences. After an introductory chapter with a rich review of the literature, Chapter 2 presents the problem to mimic the performance of a financial index considering all its components or a subset only, and it suggests a new dispersion measure of the tracking error. Chapter 3 generalizes the concept of dispersion measure reviewing the class of the coherent expectation bounded risk measures for the benchmark tracking problem. Chapter 4 deals with portfolio strategies for active management and explores the portfolio optimization problem maximizing four different performance measures.