The authors give practical implementations of order-1/2 and order-1 strong schemes for SDDEs with arbitrary fixed delays by combining linear interpolation on a fixed mesh and an augmented variable-step mesh that includes all required delay points.
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The optimal value and optimal control for the stochastic Mayer problem in markets with transaction costs are continuous under approximations of the price process in the general geometric framework with processes S and K.
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Implementation of Milstein Schemes for Stochastic Delay-Differential Equations with Arbitrary Fixed Delays
The authors give practical implementations of order-1/2 and order-1 strong schemes for SDDEs with arbitrary fixed delays by combining linear interpolation on a fixed mesh and an augmented variable-step mesh that includes all required delay points.
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On convergence of the Mayer problems arising in the theory of financial markets with transaction cost
The optimal value and optimal control for the stochastic Mayer problem in markets with transaction costs are continuous under approximations of the price process in the general geometric framework with processes S and K.