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On the Hamilton-Jacobi-Bellman equations

Lions, Pierre-Louis (1983), On the Hamilton-Jacobi-Bellman equations, Acta Applicandae Mathematicae, 1, 1, p. 17-41. http://dx.doi.org/10.1007/BF02433840

Type
Article accepté pour publication ou publié
Date
1983
Journal name
Acta Applicandae Mathematicae
Volume
1
Number
1
Publisher
Springer
Pages
17-41
Publication identifier
Metadata
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Author(s)
Lions, Pierre-Louis
Abstract (EN)
We consider general problems of optimal stochastic control and the associated Hamilton-Jacobi-Bellman equations. We recall first the usual derivation of the Hamilton-Jacobi-Bellman equations from the Dynamic Programming Principle. We then show and explain various results, including (i) continuity results for the optimal cost function, (ii) characterizations of the optimal cost function as the maximum subsolution, (iii) regularity results, and (iv) uniqueness results. We also develop the recent notion of viscosity solutions of Hamilton-Jacobi-Bellman equations.
Subjects / Keywords
Optimal stochastic control; diffusion processes; Hamilton-Jacobi-Bellman equations; viscosity solutions; Dynamic Programming Principle