Dubacova J. Stochastic Modeling in Economics and Finance

©2003 Kluwer Academic Publishers.
Preface.
Acknowledgments.
Part I Fundamentals.

Money, Capital, and Securities.
Money and Capital.
nvestment.
nterest.
Cash Flows.
Financial and Real Investment.
Securities.
Financial Market.
Financial Institutions.
Financial System.
nterest Rate.
Simple and Compound Interest.
Calendar Conventions.
Determinants of the Interest Rate.
Decomposition of the Interest Rate.
Term Structure of Interest Rates.
Continuous Compounding.
Measures of Cash Flows.
Present Value.
Annuities.
Future Value.
nteal Rate of Retu.
Duration.
Convexity.
Comparison of Investment Projects.
Yield Curves.
Retu, Expected Retu, and Risk.
Retu.
Risk Measurement.
aluation of Securities.
Coupon Bonds.
Options.
Forwards and Futures.
Matching of Assets and Liabilities.
Matching and Immunization.
Dedicated Bond Portfolio.
A Stochastic Model of Matching.
ndex Numbers and Inflation.
Construction of Index Numbers.
Stock Exchange Indicators.
nflation.
Basics of Utility Theory.
The Concept of Utility.
Utility Function.
Characteristics of Utility Functions.
Some Particular Utility Functions.
Risk Considerations.
Certainty Equivalent.
Markowitz Mean-Variance Portfolio.
Portfolio.
Construction of Optimal Portfolios and Separation Theorems.
Capital Asset Pricing Model.
Sharpe-Lintner Model.
Security Market Line.
Capital Market Line.
Arbitrage Pricing Theory.
Regression Model.
Factor Model.
Bibliographical Notes.
Part II Discrete Time Stochastic Decision Models.
ntroduction and Preliminaries.
Problem of a Private Investor.
Stochastic Dedicated Bond Portfolio.
Mathematical Programs.
Multistage Stochastic Programs.
Basic Formulations.
Scenario-Based Stochastic Linear Programs.
Horizon and Stages.
The Flower-Girl Problem.
Comparison with Stochastic Dynamic Programming.
Multiple Criteria.
Theory.
Selected Applications to Portfolio Optimization.
Multi-Objective Optimization and Stochastic Programming Models.
Selected Applications in Finance and Economics.
Portfolio Revision.
The BONDS Model.
Bank Asset and Liability Management – Model ALM.
General Features of Multiperiod Stochastic Programs in Finance.
Production Planning.
Capacity Expansion of Electric Power Generation Systems – CEP.
Unit Commitment and Economic Power Dispatch Problem.
Melt Control: Charge Optimization.
Approximation Via Scenarios.
ntroduction.
Scenarios and their Generation.
How to Draw Inference about the True Problem.
Scenario Trees for Multistage Stochastic Programs.
Case Study: Bond Portfolio Management Problem.
The Problem and the Input Data.
The Model and the Structure of the Program.
Generation of Scenarios.
Selected Numerical Results.
What if Analysis.
Discussion.
ncomplete Input Information.
Sensitivity for the Black-Scholes Formula.
Markowitz Mean-Variance Model.
ncomplete Information about Liabilities.
Numerical Techniques and Available Software (by Pavel Popela).
Motivation.
Common Optimization Techniques.
Solution Techniques for Two-Stage Stochastic Programs.
Solution Techniques for Multistage Stochastic Programs.
Approximation Techniques.
Model Management.
Bibliographical Notes.
Part III Stochastic Analysis and Diffusion Finance.
Martingales.
Stochastic Processes.
Brownian Motion and Martingales.
Markov Times and Stopping Theorem.
Local Martingales and Complete Filtrations.
and Density Theorem.
Doob-Meyer Decomposition.
Quadratic Variation of Local Martingales.
Helps to Some Exercises.
Stochastic Integration.
Stochastic Integral.
Stochastic Per Partes and Itф Formula.
Exponential Martingales and Lйvy Theorem.
Girsanov Theorem.
ntegral and Brownian Representations.
Helps to Some Exercises.
Diffusion Financial Mathematics.
Black-Scholes Calculus.
Girsanov Calculus.
Market Regulations and Option Pricing.
Helps to Some Exercises.
Bibliographical Notes.
References.