Dynamic portfolio strategies: Quantitative methods and empirical rules for incomplete information
This book investigates optimal investment problems for stochastic financial market models. It is addressed to academics and students, who are interested in the mathematics of finance, stochastic processes, optimal control, and also to practitioners in risk management and quantitative analysis who are interested in new strategies and methods of stochastic analysis. The aim of the book is to reduce the gap between model-free strategies based on ``technical analysis'' that require only historical data and strategies that are ``optimal'' for stochastic models, i.e. they are optimal only for a given model of price evolution, utility function and probability measure. The author introduces and investigates optimal investment problems for strategies that use historical prices as well as trading volume for underlying assets. Further, the author introduces a model that involves additional constraints of a very general type for the wealth process. In particular, these constraints cover the problem of replication of a given claim with a guaranteed error bound (gap). The book is divided into four parts and 13 chapters. Part I describes the stochastic market models. Part II is devoted to model-free empirical ``winning'' strategies and their statistical evaluation. Estimates of transaction costs , average performance on a probability space, piecewise constant strategies with unbounded horizon, multi-stock market and asymptotic arbitrage are considered here. Part III and IV describe optimal strategies for the diffusion market model with observable parameters and optimal strategies based on historical data for markets with nonobservable parameters, respectively. Solution of optimization problem via dynamic programming and via optimal claim, optimal portfolio compression, maximin criterion for observable but nonpredictable parameters are presented in Part III, the solution of the optimization problem for log and power utilities with historical prices and volume, the solution for general utilities and constraints via parabolic equations, special cases concerning gap and goal achieving are included into Part IV. The book contains many numerical examples, mostly based on Australian stocks data, and a lot of figures.
scientific article; zbMATH DE number 1737185