Markov chain approximation and measure change for time-inhomogeneous stochastic processes

Abstract

In this paper, we propose a general time-inhomogeneous continuous-time Markov chain (CTMC) framework for the approximation of the general one-dimensional and two-dimensional time-inhomogeneous diffusion processes. For the approximating CTMC, we can perform a change of measure, choose the minimal relative entropy measure to determine the measure uniquely, and finally establish the convergence. Therefore, the proposed methodology covers the stochastic processes that are hard to perform a change of measure, and is applicable to valuation problems driven by models not only under the risk-neutral probability measure but also under the physical probability measure.