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 inthe 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. INDICE: Preface.- 1.Some elements of stochastic analysis.- 2.Stochastic optimization problems. Examples in finance.- 3.The classical PDE approach to dynamic programming.- 4.The viscosity solutions approach to stochastic control problems.- 5.Optimal switching and free boundary problems.- 6.Backward stochastic differential equations and optimal control.- 7.Martingale and convex dualitymethods.- Appendices: A.Complements of integration.- B.Convex analysis considerations.- References.- Index.

• ISBN: 978-3-540-89499-5
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 260
• Fecha Publicación: 01/06/2009
• Nº Volúmenes: 1
• Idioma: Inglés