Optimal stochastic control and Hamilton-Jacobi-Bellman equations
P. L. Lions (1985)
Banach Center Publications
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P. L. Lions (1985)
Banach Center Publications
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Piermarco Cannarsa, Giuseppe Da Prato (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.
Salvatore Federico (2008)
Banach Center Publications
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In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund in the accumulation phase. The level of wealth is constrained to stay above a "solvency level". The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. The model is naturally formulated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach....
Beniamin Goldys (2001)
Czechoslovak Mathematical Journal
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We show that solutions to some Hamilton-Jacobi Equations associated to the problem of optimal control of stochastic semilinear equations enjoy the hypercontractivity property.
Pham, Huyên (2005)
Probability Surveys [electronic only]
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Fabio Bagagiolo (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.