Connections between stochastic control and dynamic games |
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Authors: | Paolo Dai Pra Lorenzo Meneghini Wolfgang J Runggaldier |
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Affiliation: | (1) Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy |
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Abstract: | We consider duality relations between risk-sensitive stochastic control problems and dynamic games. They are derived from
two basic duality results, the first involving free energy and relative entropy and resulting from a Legendre-type transformation,
the second involving power functions. Our approach allows us to treat, in essentially the same way, continuous- and discrete-time
problems, with complete and partial state observation, and leads to a very natural formal justification of the structure of
the cost functional of the dual. It also allows us to obtain the solution of a stochastic game problem by solving a risk-sensitive
control problem. |
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Keywords: | Risk-sensitive stochastic control Stochastic dynamic games Free energy Relative entropy Legendre-type transformations |
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