2013
DOI: 10.1080/14697688.2012.713981
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On the numerical stability of simulation methods for SDEs under multiplicative noise in finance

Abstract: When simulating discrete-time approximations of solutions of stochastic differential equations (SDEs), in particular martingales, numerical stability is clearly more important than some higher order of convergence. Discrete-time approximations of solutions of SDEs with multiplicative noise, similar to the Black-Scholes model, are widely used in simulation in finance. The stability criterion presented in this paper is designed to handle both scenario simulation and Monte Carlo simulation, i.e. both strong and w… Show more

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Cited by 3 publications
(13 citation statements)
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“…In this section we consider numerical stability issues, extending the analysis in Platen and Shi [12] to the Markovian switching case. When simulating discrete time approximations of solutions of SDEwMSs, numerical stability is clearly as important as numerical efficiency.…”
Section: Numerical Stabilitymentioning
confidence: 99%
See 4 more Smart Citations
“…In this section we consider numerical stability issues, extending the analysis in Platen and Shi [12] to the Markovian switching case. When simulating discrete time approximations of solutions of SDEwMSs, numerical stability is clearly as important as numerical efficiency.…”
Section: Numerical Stabilitymentioning
confidence: 99%
“…When simulating discrete time approximations of solutions of SDEwMSs, numerical stability is clearly as important as numerical efficiency. There have been various efforts made in the literature trying to study numerical stability for a given scheme approximating solutions of SDEs, see, for instance, Hofmann and Platen [5], Higham [4], Bruti-Liberati and Platen [3] and Platen and Shi [12]. Generally, for analyzing numerical stability, some specifically designed test equations are necessary to be introduced, the test SDEs used in the above literatures are linear SDEs with multiplicative noise defined as…”
Section: Numerical Stabilitymentioning
confidence: 99%
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