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. |
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Results 1-5 of 59
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... linear–quadratic regulator problem, and some special problems in finance theory. Otherwise, numerical methods for solving the HJB equation approximately are needed. This is the topic of Chapter IX. Chapters III, IV and VI rely on ...
... linear–quadratic regulator problem, and some special problems in finance theory. Otherwise, numerical methods for solving the HJB equation approximately are needed. This is the topic of Chapter IX. Chapters III, IV and VI rely on ...
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... linear transformation from IRn into IRd: |A| = max |x|≤1 |Ax|. The transpose of A is denoted by A . If a and A are n × n matrices, tr aA = n∑ i,j=1 a ij A ij . definite A ∈ Sn. The interior, closure, and boundary of a set B are ...
... linear transformation from IRn into IRd: |A| = max |x|≤1 |Ax|. The transpose of A is denoted by A . If a and A are n × n matrices, tr aA = n∑ i,j=1 a ij A ij . definite A ∈ Sn. The interior, closure, and boundary of a set B are ...
Page 4
... linear quadratic regulator problem considered in Example 2.3. If U = [−a, a] with a < ∞, it is an example of a linear regulator problem with a saturation constraint. One can also consider the problem of controlling the solution x(s)=( ...
... linear quadratic regulator problem considered in Example 2.3. If U = [−a, a] with a < ∞, it is an example of a linear regulator problem with a saturation constraint. One can also consider the problem of controlling the solution x(s)=( ...
Page 9
... linear quadratic regulator problem) and introduce the idea of feedback control policy. We start with a simple property of V. Let r /\ T : min(r, T). Recall that g is the boundary cost (see (3.5)). Lemma 4.1. For every initial condition ...
... linear quadratic regulator problem) and introduce the idea of feedback control policy. We start with a simple property of V. Let r /\ T : min(r, T). Recall that g is the boundary cost (see (3.5)). Lemma 4.1. For every initial condition ...
Page 13
... Example 5.1. Consider the linear quadratic regulator problem (LQRP) described in Example 2.3. In this example, O : R”, U : 1Rm,Z/l(t,:L') : Z/I0 (t), and f(t, av, v) : A(t)a3 + B(t)'u (5.10) L(t, 910,11) : .1:-M(t)w + '0 - N(t)v W(t,5c) ...
... Example 5.1. Consider the linear quadratic regulator problem (LQRP) described in Example 2.3. In this example, O : R”, U : 1Rm,Z/l(t,:L') : Z/I0 (t), and f(t, av, v) : A(t)a3 + B(t)'u (5.10) L(t, 910,11) : .1:-M(t)w + '0 - N(t)v W(t,5c) ...
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