Frontiers in Applied Mathematics and Statistics (Jul 2024)
A discrete-time model that weakly converges to a continuous-time geometric Brownian motion with Markov switching drift rate
Abstract
This research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 × 2 Markov chain. A discrete-time multiplicative approximation scheme was developed, and its convergence in Skorokhod topology to the continuous-time geometric Brownian motion with switching has been proved. Furthermore, in a financial market where the discounted asset price follows a geometric Brownian motion with drift switching, market incompleteness was established, and multiple equivalent martingale measures were constructed.
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