Journal ArticleDOI
Some Results on Risk-Sensitive Control with Full Observation
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In this paper, the Bellman equation of the risk sensitive control problem with full observation is considered, and it appears as an example of a quasi-linear parabolic equation in the whole space and fairly general growth assumptions with respect to the space variable x are permitted.Abstract:
The Bellman equation of the risk-sensitive control problem with full observation is considered. It appears as an example of a quasi-linear parabolic equation in the whole space, and fairly general growth assumptions with respect to the space variable x are permitted. The stochastic control problem is then solved, making use of the analytic results. The case of large deviation with small noises is then treated, and the limit corresponds to a differential game.read more
Citations
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Journal ArticleDOI
BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations
N. El-Karoui,S. Hamadène +1 more
TL;DR: In this article, the authors deal with the risk-sensitive control, zero-sum and non-zero-sum game problems of stochastic functional differential equations, and they show the existence of an optimal control and, a saddle-point and an equilibrium point for respectively the zero sum and non zero sum games.
Proceedings Article
Risk sensitive path integral control
TL;DR: In this article, the authors show that path integral methods generalize directly to risk sensitive stochastic optimal control with non-linear dynamics in continuous space-time, and demonstrate the effect of multi-modal control with risk sensitivity.
Journal ArticleDOI
Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model
Mark H. A. Davis,Sebastien Lleo +1 more
TL;DR: The main result of this paper is to show that the risk-sensitive jump-diffusion problem can be fully characterized in terms of a parabolic Hamilton-Jacobi-Bellman PDE rather than a partial integro-differential equation, and that this PDE admits a classical $(C^{1,2})$ solution.
Book ChapterDOI
Solving long term optimal investment problems with Cox-Ingersoll-Ross interest rates
Hiroaki Hata,Jun Sekine +1 more
TL;DR: In this article, a large deviations control problem is treated for a long term optimal investment on a financial market with a bank account and a risky stock, both of which are affected by a stochastic factor described as Cox-Ingersoll-Ross's interest rates.
Journal ArticleDOI
Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions
Ari Arapostathis,Anup Biswas +1 more
TL;DR: In this article, the authors considered the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift, and showed that there always exists a solution to the risk sensitive Hamilton-Jacobi-Bellman (HJB) equation.