Space-grid approximations of hybrid stochastic differential equations and first-passage properties
Year: 2025
Type: article
Abstract: Hybrid stochastic differential equations (SDEs) are a useful tool for modeling continuously varying stochastic systems modulated by a random environment, which may depend on the system state itself. In this paper we establish the pathwise convergence of solutions to hybrid SDEs using space-grid discretizations. Though time-grid discretizations are a classical approach for simulation purposes, our space-grid discretization provides a link with multi-regime Markov-modulated Brownian motions. This connection allows us to explore aspects that have been largely unexplored in the hybrid SDE literature. Specifically, we exploit our convergence result to obtain efficient and computationally tractable approximations for first-passage probabilities and expected occupation times of the solutions to hybrid SDEs. Lastly, we illustrate the effectiveness of the resulting approximations through numerical examples.
Source: Journal of Applied Probability
Authors: Hansjoerg Albrecher, Oscar Peralta
Institutions: University of Lausanne, Cornell University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4417490075