## Controlled Markov Processes and Viscosity SolutionsThis book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games. |

### From inside the book

Results 1-5 of 60

Page

However, under quite general assumptions the value function is the

However, under quite general assumptions the value function is the

**unique**viscosity solution of the HJB equation with appropriate boundary conditions. Page 3

It is often assumed that h and ψ are convex functions, and that h(x), ψ(x) have a

It is often assumed that h and ψ are convex functions, and that h(x), ψ(x) have a

**unique**minimum at x = 0. A typical example of h is h(x) = n∑i=1 [ αi (xi )+ ... Page 5

... t ≤ s ≤ t1 with initial condition (3.3) x(t) = x has a

... t ≤ s ≤ t1 with initial condition (3.3) x(t) = x has a

**unique**I. Deterministic Optimal Control 5 Finite time horizon problems. Page 6

with initial condition (3.3) x(t) = x has a

with initial condition (3.3) x(t) = x has a

**unique**solution. The solution x(s) of (3.2) and (3.3) is called the state of the system at time s. Page 14

For later use, we note that the

For later use, we note that the

**unique**maximizer of (5.12) is (5.13) 11* I -%N*1(1s)B'(t)p. To use the Verification Theorem 5.1, first we have to solve ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

Viscosity Solutions | 57 |

Differential Games | 375 |

A Duality Relationships 397 | 396 |

References | 409 |

### Other editions - View all

Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |

### Common terms and phrases

admissible control assume assumptions boundary condition boundary data bounded brownian motion calculus of variations Chapter classical solution consider constant controlled Markov diffusion convergence convex Corollary cost function deﬁne deﬁnition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit ﬁnite ﬁrst formulation G Q0 Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation progressively measurable proof of Theorem prove reference probability system Remark result risk sensitive satisﬁes satisfying Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose Theorem 9.1 uniformly continuous unique value function Veriﬁcation Theorem viscosity solution viscosity subsolution viscosity supersolution