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- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/BF02433840
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: May 24, 2006