Displaying similar documents to “On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions.”

On an infinite dimensional linear-quadratic problem with fixed endpoints: the continuity question

K. Maciej Przyłuski (2014)

International Journal of Applied Mathematics and Computer Science

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In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Target achieving portfolio under model misspecification: quadratic optimization framework

Dariusz Zawisza (2012)

Applicationes Mathematicae

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We incorporate model uncertainty into a quadratic portfolio optimization framework. We consider an incomplete continuous time market with a non-tradable stochastic factor. Two stochastic game problems are formulated and solved using Hamilton-Jacobi-Bellman-Isaacs equations. The proof of existence and uniqueness of a solution to the resulting semilinear PDE is also provided. The latter can be used to extend many portfolio optimization results.

A deterministic affine-quadratic optimal control problem

Yuanchang Wang, Jiongmin Yong (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton–Jacobi–Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some...

Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints

Nikolai P. Osmolovskii (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints they guarantee the bounded strong quadratic...

Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints

Nikolai P. Osmolovskii (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints...

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

Freddy Delbaen, Ying Hu, Adrien Richou (2011)

Annales de l'I.H.P. Probabilités et statistiques

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In [ (2008) 543–567], the authors proved the uniqueness among the solutions of quadratic BSDEs with convex generators and unbounded terminal conditions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman–Kac formula proved in...