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.
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Accepted 25 March 1996
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Bensoussan, A., Frehse, J. & Nagai, H. Some Results on Risk-Sensitive Control with Full Observation. Appl Math Optim 37, 1–41 (1998). https://doi.org/10.1007/s002459900067
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DOI: https://doi.org/10.1007/s002459900067