Abstract
In this paper, we present a finite difference scheme for a linear complementarity problem with a mixed boundary condition arising from pricing a Russian option with a finite time horizon. An implicit Euler method for the temporal discretization and second-order difference schemes on a piecewise uniform mesh for the spatial discretization are used to solve the linear complementarity problem with a mixed boundary condition. It is shown that the transformed discrete operator satisfies a maximum principle, which is used to derive the error estimate. It is proved that the scheme is first- and second-order convergent with respect to the temporal and spatial variables, respectively. Numerical experiments verify the validity of the theoretical results.
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