Markov Decision Processes with Applications to Finance

✍ Scribed by Nicole Bäuerle, Ulrich Rieder (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 405
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and at the same time show its application by means of numerous examples, mostly taken from the fields of finance and operations research. By using a structural approach many technicalities (concerning measure theory) are avoided. They cover problems with finite and infinite horizons, as well as partially observable Markov decision processes, piecewise deterministic Markov decision processes and stopping problems.

The book presents Markov decision processes in action and includes various state-of-the-art applications with a particular view towards finance. It is useful for upper-level undergraduates, Master's students and researchers in both applied probability and finance, and provides exercises (without solutions).

✦ Table of Contents

Front Matter....Pages i-xvi
Introduction and First Examples....Pages 1-9
Front Matter....Pages 11-11
Theory of Finite Horizon Markov Decision Processes....Pages 13-57
The Financial Markets....Pages 59-74
Financial Optimization Problems....Pages 75-144
Front Matter....Pages 145-145
Partially Observable Markov Decision Processes....Pages 147-174
Partially Observable Markov Decision Problems in Finance....Pages 175-189
Front Matter....Pages 191-191
Theory of Infinite Horizon Markov Decision Processes....Pages 193-242
Piecewise Deterministic Markov Decision Processes....Pages 243-265
Optimization Problems in Finance and Insurance....Pages 267-299
Front Matter....Pages 301-301
Theory of Optimal Stopping Problems....Pages 303-330
Stopping Problems in Finance....Pages 331-343
Front Matter....Pages 345-345
Tools from Analysis....Pages 347-354
Tools from Probability....Pages 355-363
Tools from Mathematical Finance....Pages 365-368
Back Matter....Pages 369-388

✦ Subjects

Probability Theory and Stochastic Processes; Quantitative Finance; Applications of Mathematics