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References (30)
-
H. Soner (1986)
Optimal control with state-space constraint ISiam Journal on Control and Optimization, 24
-
W. Fleming, P. Lions (1988)
Stochastic differential systems, stochastic control theory and applications -
N. Framstad, B. Øksendal, A. Sulem (2004)
Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to FinanceJournal of Optimization Theory and Applications, 121
-
H. Pham (1998)
Optimal stopping of controlled jump diffusion processes: A viscosity solution approachJ. Math. Syst. Estim. Control, 8
-
R. Situ (2005)
Theory of Stochastic Differential Equations with Jumps and Applications -
J. Bismut (1978)
An Introductory Approach to Duality in Optimal Stochastic ControlSiam Review, 20
-
A. Sayah (1991)
Équations d’Hamilton-Jacobi du premier ordre avec termes intégre-différentiels, I. Unicité des solutions de viscosité, II. Existence de solutions de viscositéCommun. Partial Differ. Equ., 16
-
G. Barles, C. Imbert (2007)
Second-order elliptic integro-differential equations: viscosity solutions' theory revisitedAnnales De L Institut Henri Poincare-analyse Non Lineaire, 25
-
J.M. Yong (1992)
Dynamic Programming Method and the Hamilton-Jacobi-Bellman Equations -
G. Barles, R. Buckdahn, É. Pardoux (1997)
Backward stochastic differential equations and integral-partial differential equationsStochastics and Stochastics Reports, 60
-
J.M. Bismut (1978)
An introductory approach to duality in optimal stochastic controlSIAM J. Control Optim., 20
-
J. Yong, X. Zhou (1999)
Stochastic Controls: Hamiltonian Systems and HJB Equations -
Imran Biswas, E. Jakobsen, K. Karlsen (2010)
Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion ProcessesApplied Mathematics and Optimization, 62
-
A. Bensoussan (1982)
Lectures on stochastic control -
Juan Li, S. Peng (2009)
Stochastic optimization theory of backward stochastic differential equations with jumps and viscosity solutions of Hamilton–Jacobi–Bellman equationsNonlinear Analysis-theory Methods & Applications, 70
-
M. Arisawa (2007)
Corrigendum for the comparison theorems in: “A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations” [Ann. I. H. Poincaré – AN 23 (5) (2006) 695–711]Annales De L Institut Henri Poincare-analyse Non Lineaire, 24
-
R. Situ (2005)
Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering -
Sayah Awatif (1991)
Equqtions D'Hamilton-Jacobi Du Premier Ordre Avec Termes Intégro-Différentiels: Partie II: Unicité Des Solutions De ViscositéCommunications in Partial Differential Equations, 16
-
U. Haussmann (1981)
On the Adjoint Process for Optimal Control of Diffusion ProcessesSiam Journal on Control and Optimization, 19
-
X. Zhou, J. Yong, Xunjing Li (1997)
Stochastic Verification Theorems within the Framework of Viscosity SolutionsSiam Journal on Control and Optimization, 35
-
B. Øksendal, A. Sulem (2005)
Applied Stochastic Control of Jump Diffusions -
L. Rogers (1982)
Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00European Journal of Operational Research, 10
-
Shanjian Tang, Xunjing Li (1994)
Necessary Conditions for Optimal Control of Stochastic Systems with Random JumpsSiam Journal on Control and Optimization, 32
-
Fausto Gozzi, A. Swiech, X. Zhou (2010)
Erratum: "A Corrected Proof of the Stochastic Verification Theorem within the Framework of Viscosity Solutions"SIAM J. Control. Optim., 48
-
N. Ikeda, S. Watanabe (1989)
Stochastic Differential Equations and Diffusion Processes -
Xun Zhouf (1990)
The connection between the maximum principle and dynamic programming in stochastic controlStochastics and Stochastics Reports, 31
-
M. Arisawa (2006)
A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equationsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 23
-
O. Alvarez, A. Tourin (1996)
Viscosity solutions of nonlinear integro-differential equationsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 13
-
E. Jakobsen, K. Karlsen (2006)
A “maximum principle for semicontinuous functions” applicable to integro-partial differential equationsNonlinear Differential Equations and Applications NoDEA, 13
-
H. Soner (1988)
Optimal Control of Jump-Markov Processes and Viscosity Solutions, 10
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer Science+Business Media, LLC
- Subject
- Mathematics; Numerical and Computational Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-010-9115-8
- Publisher site
- See Article on Publisher Site
Abstract
This paper is concerned with the stochastic optimal control problem of jump diffusions. The relationship between stochastic maximum principle and dynamic programming principle is discussed. Without involving any derivatives of the value function, relations among the adjoint processes, the generalized Hamiltonian and the value function are investigated by employing the notions of semijets evoked in defining the viscosity solutions. Stochastic verification theorem is also given to verify whether a given admissible control is optimal.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Apr 1, 2011