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 6-10 of 74
Page 3
... finite time interval t≤s ≤ t1 . Given an initial inventory x ( t ) = x , the problem is to choose the production rate u ( s ) to minimize ( 2.2 ) t1 h ( x ( s ) ) ds + 4 ( x ( t1 ) ) . We call t1 the terminal time , h the running cost ...
... finite time interval t≤s ≤ t1 . Given an initial inventory x ( t ) = x , the problem is to choose the production rate u ( s ) to minimize ( 2.2 ) t1 h ( x ( s ) ) ds + 4 ( x ( t1 ) ) . We call t1 the terminal time , h the running cost ...
Page 4
... finite time interval t ≤ s ≤ t1 . An initial position and velocity (x1 (t),x 2 (t)) = (x1 ,x2 ) are given. We seek to minimize a quadratic criterion of the form (2.5) ∫ t1 t [ m1 ] ds + d1 )2, x1 (s)2 + m2x2 (s)2 + u(s)2 x1 (t1 )2 + ...
... finite time interval t ≤ s ≤ t1 . An initial position and velocity (x1 (t),x 2 (t)) = (x1 ,x2 ) are given. We seek to minimize a quadratic criterion of the form (2.5) ∫ t1 t [ m1 ] ds + d1 )2, x1 (s)2 + m2x2 (s)2 + u(s)2 x1 (t1 )2 + ...
Page 5
... Finite time horizon problems In this section we formulate some classes of deterministic optimal control problems , which will be studied in the rest of this chapter and in Chapter II . At the end of the section , each of these classes ...
... Finite time horizon problems In this section we formulate some classes of deterministic optimal control problems , which will be studied in the rest of this chapter and in Chapter II . At the end of the section , each of these classes ...
Page 6
... finite time horizon . The problem is to find u ( · ) € U ° ( t ) which minimizes ( 3.4 ) • t1 J ( t , x ; u ) = [ * L ( 8 , x ( s ) , u ( s ) ) ds + ( ( x ( 11 ) ) , t where L = C ( Qo × U ) . We call L the running cost function and the ...
... finite time horizon . The problem is to find u ( · ) € U ° ( t ) which minimizes ( 3.4 ) • t1 J ( t , x ; u ) = [ * L ( 8 , x ( s ) , u ( s ) ) ds + ( ( x ( 11 ) ) , t where L = C ( Qo × U ) . We call L the running cost function and the ...
Page 15
... finite interval , which excludes the possibility that tmin > ∞ . · In Section VI.8 we will encounter a class of problems in which M ( s ) is negative definite . Such problems are called LQRP problems with indefinite sign . In this case ...
... finite interval , which excludes the possibility that tmin > ∞ . · In Section VI.8 we will encounter a class of problems in which M ( s ) is negative definite . Such problems are called LQRP problems with indefinite sign . In this case ...
Contents
1 | |
Viscosity Solutions | 57 |
Classical Solutions119 | 118 |
Controlled Markov Diffusions in R | 151 |
SecondOrder Case | 199 |
Logarithmic Transformations and Risk Sensitivity | 227 |
Singular Perturbations 261 | 260 |
Singular Stochastic Control | 293 |
Finite Difference Numerical Approximations | 321 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
Index 425 | 424 |
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 C₁ C¹(Q calculus of variations Chapter classical solution consider constant constraint controlled Markov diffusion convergence convex Corollary defined definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formulation given Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes 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 Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose t₁ Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution