Controlled Markov Processes and Viscosity SolutionsThis book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. |
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Page 3
... cost , and the terminal cost . It is often assumed that h and are convex functions , and that h ( x ) , v ( x ) have a unique minimum at x = 0. A typical example of h is n h ( x ) = Σ [ ai ( xi ) ++ Yi ( Xi ) ̄ ] , i = 1 where a1 , Yi ...
... cost , and the terminal cost . It is often assumed that h and are convex functions , and that h ( x ) , v ( x ) have a unique minimum at x = 0. A typical example of h is n h ( x ) = Σ [ ai ( xi ) ++ Yi ( Xi ) ̄ ] , i = 1 where a1 , Yi ...
Page 129
... cost func- tion and a terminal cost function . Formula ( 2.10 ) expresses ( t , x ) as a total expected cost over the time interval [ t , t1 ] . III.3 Autonomous ( time - homogeneous ) Markov processes Let us now take Io = I = [ 0 ...
... cost func- tion and a terminal cost function . Formula ( 2.10 ) expresses ( t , x ) as a total expected cost over the time interval [ t , t1 ] . III.3 Autonomous ( time - homogeneous ) Markov processes Let us now take Io = I = [ 0 ...
Page 339
... cost , which is linearly proportional in the size of the trans- action . Let μ Є ( 0,1 ) be the cost of transaction from stock to bond . In this model , we also allow transactions from bond to stock with a linear transaction cost . Let ...
... cost , which is linearly proportional in the size of the trans- action . Let μ Є ( 0,1 ) be the cost of transaction from stock to bond . In this model , we also allow transactions from bond to stock with a linear transaction cost . Let ...
Other editions - View all
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Limited preview - 2006 |
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 c₁ Cą(Q calculus of variations Chapter classical solution consider constant continuous on Q convergence convex Corollary cylindrical region defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data lateral boundary Lemma lim sup 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 proof of Theorem prove result satisfies second-order Section semigroup stochastic differential equation Suppose t₁ test function Theorem 5.1 uniformly continuous unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields