Continuous-time Stochastic Control and Optimization with Financial Applications

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 toknow more about the use of stochastic optimization methods in finance.

List of contents

Some elements of stochastic analysis.- Stochastic optimization problems. Examples in finance.- The classical PDE approach to dynamic programming.- The viscosity solutions approach to stochastic control problems.- Optimal switching and free boundary problems.- Backward stochastic differential equations and optimal control.- Martingale and convex duality methods.

Product details

• Authors: Huyên Pham
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 19.10.2010
• EAN: 9783642100444
• ISBN: 978-3-642-10044-4
• No. of pages: 232
• Weight: 381 g
• Illustrations: XVII, 232 p.
• Series: Stochastic Modelling and Applied Probability
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; B, Optimization, Game Theory, Economics, Social and Behav. Sciences, Mathematics and Statistics, game theory, Finance & accounting, Probability Theory and Stochastic Processes, Systems Theory, Control, Probabilities, Stochastics, Probability Theory, Economics, Mathematical, Quantitative Finance, Mathematics in Business, Economics and Finance, Mathematical optimization, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, System Theory, Cybernetics & systems theory, Cybernetics and systems theory