Abstract
We are concerned with an optimal stochastic control and stopping pro- blem of a jump diffusion process. The main interest of this paper lies in the case where the dynamics has infinite variance, especially in the case of solutions of SDEs driven by symmetric stable processes. We prove that the value function is a viscosity solution of the integro-differential variational inequality arising from the associated dynamic program- ming. We also establish comparison principles in the class of semi-continuous functions with polynomial growth of a given order. Mathematics Subject Classication 2000: 93E20, 49L25, 60J75.
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