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In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary...
It holds in great generality that a plan is optimal for a dynamic programming problem, if and only if it is “thrifty” and “equalizing.” An alternative characterization of an optimal plan, that applies in many economic models, is that the plan must satisfy an appropriate Euler equation and a...
We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also some shell models of turbulence. We state the existence and uniqueness theorem for the class...
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the...
We prove the uniqueness of the viscosity solution of an Isaacs quasi-variational inequality arising in an impulse control minimax problem, motivated by an application in mathematical finance.
This paper deals with a class of semi-Markov control models with Borel state and control spaces, possibly unbounded costs, and unknown holding times distribution F . Assuming that F does not depend on state-action pairs, we combine suitable methods of statistical estimation of the mean holding...
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