The optimal control of a two-parameter jump process

1986 ◽  
Vol 26 (1) ◽  
pp. 77-87
Author(s):  
Ata Al-Hussaini ◽  
R. J. Elliott
Keyword(s):  
Optimal Control ◽  
Jump Process ◽  
Two Parameter

scholarly journals Backward SDEs and infinite horizon stochastic optimal control

2019 ◽  
Vol 25 ◽  
pp. 31 ◽  
Author(s):  
Fulvia Confortola ◽  
Andrea Cosso ◽  
Marco Fuhrman
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Stochastic Differential Equation ◽  
Control Problem ◽  
Backward Stochastic Differential Equation ◽  
Infinite Horizon ◽  
Jump Process ◽  
Elliptic Type

We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients, both with respect to state and control, and the noise can be degenerate. We prove that the value, i.e. the supremum of the reward functional over all admissible controls, can be represented by the solution of an associated backward stochastic differential equation (BSDE) driven by the Brownian motion and an auxiliary independent Poisson process and having a sign constraint on jumps. In the Markovian case when the coefficients depend only on the present values of the state and the control, we prove that the BSDE can be used to construct the solution, in the sense of viscosity theory, to the corresponding Hamilton-Jacobi-Bellman partial differential equation of elliptic type on the whole space, so that it provides us with a Feynman-Kac representation in this fully nonlinear context. The method of proof consists in showing that the value of the original problem is the same as the value of an auxiliary optimal control problem (called randomized), where the control process is replaced by a fixed pure jump process and maximization is taken over a class of absolutely continuous changes of measures which affect the stochastic intensity of the jump process but leave the law of the driving Brownian motion unchanged.

Optimal control of a jump process

1977 ◽  
Vol 40 (3) ◽  
pp. 183-202 ◽  
Author(s):  
Mark Davis ◽  
Robert Elliott
Keyword(s):  
Optimal Control ◽  
Jump Process

Optimal control of a two-parameter system in a Hilbert space

1999 ◽  
Vol 97 (2) ◽  
pp. 3908-3916
Author(s):  
I. V. Gaishun ◽  
M. P. Dymkov
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Parameter System ◽  
Two Parameter

scholarly journals Filtrations for the two parameter jump process

1985 ◽  
Vol 16 (1) ◽  
pp. 118-139 ◽  
Author(s):  
Ata Al-Hussaini ◽  
Robert J. Elliott
Keyword(s):  
Jump Process ◽  
Two Parameter
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