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Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

2023/03/10 by Paweł Przybyłowicz, Przybyłowicz, Paweł, Verena Schwarz +3
Economics, Econometrics and Finance · Social Sciences · Decision Sciences · #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management #demographic modeling and climate adaptation

paper · pdf · doi:10.48550/arxiv.2303.05945

Abstract

In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes and provide lower error bounds of order 3/4 for both classes of approximation schemes. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

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