Probabilistic and percentile/quantile functions play an important role in several applications, such as finance (Value-at-Risk), nuclear safety, and the environment. Recently, significant advances have been made in sensitivity analysis and optimization of probabilistic functions, which is the basis for construction of new efficient approaches. This book presents the state of the art in the theory of optimization of probabilistic functions and several engineering and finance applications, including material flow systems, production planning, Value-at-Risk, asset and liability management, and optimal trading strategies for financial derivatives (options). Audience: The book is a valuable source of information for faculty, students, researchers, and practitioners in financial engineering, operation research, optimization, computer science, and related areas.
Table of ContentsPreface. Introduction to the Theory of Probabilistic Functions and Percentiles; S. Uryasev. Pricing American Options by Simulation Using a Shastic Mesh with Optimized Weights; M. Broadie, et al. On Optimization of Unreliable Material Flow Systems; Y. Ermoliev, et al. Shastic Optimization in Asset & Liability Management: A Model for Non-Maturing Accounts; K. Frauendorfer, M. Schürle. Optimization in the Space of Distribution Functions and Applications in the Bayes Analysis; A.N. Golodnikov, et al. Sensitivity Analysis of Worst-Case Distribution for Probability Optimization Problems; Y.S. Kan, A.I. Kibzun. On Maximum Realiability Problem in Parallel-Series Systems with Two Failure Modes; V. Kirilyuk. Robust Monte Carlo Simulation for Approximate Covariance Matrices and VaR Analyses; A. Kreinin, A. Levin. Structure of Optimal Stopping Strategies for American Type Options; A.G. Kukush, D.S. Silvestrov. Approximation of Value-at-Risk Problems with Decision Rules; R. Lepp. Managing Risk with Expected Shortfall; H. Mausser, D. Rosen. On the Numerical Solution of Jointly Chance Constrained Problems; J. Mayer. Management of Quality of Service through Chance-constraints in Multimedia Networks; E.A. Medova, J.E. Scott. Solution of a Product Substitution Problem Using Shastic Programming; M.R. Murr, A. Prékopa. Some Remarks on the Value-at-Risk and the Conditional Value-at-risk; G.Ch. Pflug. Statistical Inference of Shastic Optimization Problems; A. Shapiro.