Stochastic Optimal Control in Finance PDF

Of course, optimal control is at the core of math finance. Take few applications: Option Pricing: you have an exposure to a time dependent combination of market factors; you have some knowledge of their dynamics. They are partly deterministic, partly stochastic (i.e. random). At each "time step" you can adjust your portfolio at a given cost.

Stochastic Optimal Control with Finance Applications Tomas Bj¨ork, Department of Finance, Stockholm School of Economics, KTH, February, 2010 Tomas Bjork, 2010 1 Usually, the dynamics of the economic or finance systems are modeled via a Stochastic Differential Equation (SDE) . Therefore, for controlling such a problem, one can use a Stochastic Optimal Control (SOC) method. Merton portfolio allocation problem is such a problem .

This book focuses on the interaction between equilibrium real exchange rates, optimal external debt, endogenous optimal growth, and current account balances in a world of uncertainty. The theoretical parts result from interdisciplinary research between economics and state of the art applied mathematics. From the economic theory and the mathematics of stochastic optimal control, benchmarks are I have co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, 1993 (second edition in 2006), and authored or co-authored several articles on nonlinear partial differential equations, viscosity solutions, stochastic optimal control and mathematical finance.

stochastic control and optimal stopping problems. The remaining part of the lectures focus on the more recent literature on stochastic control, namely stochastic target problems. These problems are moti-vated by the superhedging problem in nancial mathematics. Various extensions have been studied in … Stochastic Optimal Control in Finance è un libro di Soner Mete H. pubblicato da Scuola Normale Superiore (EN) nella collana Cattedra galileiana - ISBN: 9788876421396

Classical approach to stochastic control: Show if possible the existence of a smooth solution to HJB, or even better obtain an explicit solution Veri cation step: prove that this smooth solution to HJB is the value function of the stochastic control problem, and obtain as a byproduct the optimal control. Remark. This article is concerned with a risk-sensitive stochastic optimal control problem motivated by a kind of optimal portfolio choice problem in the financial market. The maximum principle for this kind of problem is obtained, which is similar in form to its risk-neutral counterpart.