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 55
Page 2
... initial data. See Section 4, and also Section 7 for infinite time horizon problems. The value function V for a deterministic optimal control problem satisfies, at least formally, a first order nonlinear partial differential equation ...
... initial data. See Section 4, and also Section 7 for infinite time horizon problems. The value function V for a deterministic optimal control problem satisfies, at least formally, a first order nonlinear partial differential equation ...
Page 6
... initial data (t, x) a set U(t, x) ⊂ U0(t) of admissible controls and a payoff functional J(t, x;u) to be minimized. Let us first formulate some particular classes of problems (A through D below). Then we subsume all of these classes in ...
... initial data (t, x) a set U(t, x) ⊂ U0(t) of admissible controls and a payoff functional J(t, x;u) to be minimized. Let us first formulate some particular classes of problems (A through D below). Then we subsume all of these classes in ...
Page 8
... initial condition :Z(t) : at. Then we assume that (3-9) 11s(-) E 7/{(8, H2 ... data (t, at) G Q, find u* G Z/l(t,a3) such that J(t,5c; u*) § J(t,ac;u) for ... first term on the right side by J'(t, cc; J' is the payoff for the problem of ...
... initial condition :Z(t) : at. Then we assume that (3-9) 11s(-) E 7/{(8, H2 ... data (t, at) G Q, find u* G Z/l(t,a3) such that J(t,5c; u*) § J(t,ac;u) for ... first term on the right side by J'(t, cc; J' is the payoff for the problem of ...
Page 12
... data are (5.5) V(t1,:1;) : 1b(:1;), cc G IR". We now state a theorem which connects the dynamic programming equation ... initial data (t, ac) and W(t,a3) : V(t, In Theorem 5.1, denotes the solution to (3.2) with :u*(-), 12 1 ...
... data are (5.5) V(t1,:1;) : 1b(:1;), cc G IR". We now state a theorem which connects the dynamic programming equation ... initial data (t, ac) and W(t,a3) : V(t, In Theorem 5.1, denotes the solution to (3.2) with :u*(-), 12 1 ...
Page 15
... data (5.16), without reference to the initial conditions for x(s). This is one of the important aspects of the LQRP. In the LQRP as formulated in Example 2.3, the matrices M(s) and D are nonnegative definite and N(s) is positive ...
... data (5.16), without reference to the initial conditions for x(s). This is one of the important aspects of the LQRP. In the LQRP as formulated in Example 2.3, the matrices M(s) and D are nonnegative definite and N(s) is positive ...
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