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Abstract
We consider a broad class of singular stochastic control problems of spectrally negative jump diffusions in the presence of potentially nonlinear state-dependent exercise payoffs. We analyse these problems by relying on associated variational inequalities and state a set of sufficient conditions under which the value of the considered problems can be explicitly derived in terms of the increasing minimal r-harmonic map. We also present a set of inequalities bounding the value of the optimal policy and prove that increased policy flexibility increases both the value of the optimal strategy as well as the rate at which this value grows.
Acknowledgements
The authors are grateful to an anonymous referee for helpful comments. The financial support from the Foundation for the Promotion of the Actuarial Profession, the Finnish Insurance Society, and the Research Unit of Economic Structures and Growth (RUESG) at the University of Helsinki to Luis H.R. Alvarez is gratefully acknowledged. Both authors gratefully acknowledge the financial support from OP Bank Research Foundation.