On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions.
Baten, Md.Azizul (2005)
Lobachevskii Journal of Mathematics
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Baten, Md.Azizul (2005)
Lobachevskii Journal of Mathematics
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Stefan Ankirchner, Thomas Kruse (2015)
Banach Center Publications
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We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the...
Zenghu Li, Leonid Mytnik (2011)
Annales de l'I.H.P. Probabilités et statistiques
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General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada–Watanabe type. The results are applied to stochastic equations driven by spectrally positive Lévy processes.
Pham, Huyên (2005)
Probability Surveys [electronic only]
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Olivier Alvarez, Agnès Tourin (1996)
Annales de l'I.H.P. Analyse non linéaire
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Zhiyong Yu (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with...