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This is an overview of the work of the authors and their collaborators on thecharacterization of risk sensitive costs and rewards in terms of an abstractCollatz-Wielandt formula and in case of rewards, also a controlled version ofthe Donsker-Varadhan formula. For the finite state and action case, this leadsto useful linear and dynamic programming formulations in the reducible case.

`Controlled' versions of the Collatz-Wielandt and Donsker-Varadhan formulae