Continuous-time Stochastic Control and Optimization with Financial Applications

✍ Scribed by Huyên Pham (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Tongue: English
Leaves: 243
Series: Stochastic Modelling and Applied Probability 61
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control.

This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc.

This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

✦ Table of Contents

Front Matter....Pages 1-17
Some elements of stochastic analysis....Pages 1-26
Stochastic optimization problems. Examples in finance....Pages 27-35
The classical PDE approach to dynamic programming....Pages 37-60
The viscosity solutions approach to stochastic control problems....Pages 61-94
Optimal switching and free boundary problems....Pages 95-137
Backward stochastic differential equations and optimal control....Pages 139-169
Martingale and convex duality methods....Pages 171-212
Back Matter....Pages 213-234

✦ Subjects

Calculus of Variations and Optimal Control; Optimization; Game Theory, Economics, Social and Behav. Sciences; Systems Theory, Control; Probability Theory and Stochastic Processes; Quantitative Finance

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