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Multi-stage Euler-Maruyama methods for backward stochastic differential equations driven by continuous-time Markov chains

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  • Akihiro Kaneko

Abstract

Numerical methods for computing the solutions of Markov backward stochastic differential equations (BSDEs) driven by continuous-time Markov chains (CTMCs) are explored. The main contributions of this paper are as follows: (1) we observe that Euler-Maruyama temporal discretization methods for solving Markov BSDEs driven by CTMCs are equivalent to exponential integrators for solving the associated systems of ordinary differential equations (ODEs); (2) we introduce multi-stage Euler-Maruyama methods for effectively solving "stiff" Markov BSDEs driven by CTMCs; these BSDEs typically arise from the spatial discretization of Markov BSDEs driven by Brownian motion; (3) we propose a multilevel spatial discretization method on sparse grids that efficiently approximates high-dimensional Markov BSDEs driven by Brownian motion with a combination of multiple Markov BSDEs driven by CTMCs on grids with different resolutions. We also illustrate the effectiveness of the presented methods with a number of numerical experiments in which we treat nonlinear BSDEs arising from option pricing problems in finance.

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  • Akihiro Kaneko, 2023. "Multi-stage Euler-Maruyama methods for backward stochastic differential equations driven by continuous-time Markov chains," Papers 2311.08826, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2311.08826
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    References listed on IDEAS

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