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Full-Text Articles in Physical Sciences and Mathematics
On The Impulse Control Of Jump Diffusions, Erhan Bayraktar, Thomas Emmerling, José-Luis Menaldi
On The Impulse Control Of Jump Diffusions, Erhan Bayraktar, Thomas Emmerling, José-Luis Menaldi
Mathematics Faculty Research Publications
Regularity of the impulse control problem for a nondegenerate n-dimensional jump diffusion with infinite activity and finite variation jumps was recently examined in [M. H. A. Davis, X. Guo, and G. Wu, SIAM J. Control Optim., 48 (2010), pp. 5276–5293]. Here we extend the analysis to include infinite activity and infinite variation jumps. More specifically, we show that the value function u of the impulse control problem satisfies u ∈ Wloc2,p(Rn).
Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi
Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi
Mathematics Faculty Research Publications
We consider the solution of a stochastic integral control problem, and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W1,∞(Ο),
where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.
Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi
Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi
Mathematics Faculty Research Publications
We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W1,∞(Ο),
where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.