Convergence of $theta$ Euler-Maruyama method for SDEs in Mathematical finance
کد مقاله : 1124-FEMATH (R1)
مینو کامرانی *
دانشگاه رازی
چکیده مقاله:
In this paper we are interested in approximation of stochastic differential equations which have non-lipschitz coefficients. Motivation comes from finance and biology where many widely applied modelsndo not satisfy the standard assumptions required for the strong convergence. Simplenexamples show that, for example, the Euler-Maruyama scheme may not converge eithernin the strong or weak sense when the standard assumptions do not hold. Nevertheless,nnew convergence results have been obtained recently for many such models in financialnmathematics. In this paper we apply $theta$-Euler-Maruyama method and we show that this method under some conditions is convergence and also it preserve the domain of the SDE. n Moreover, we conclude this result can be applied to many SDEs we encounternin mathematical finance and bio-mathematics such as CEV and CIR models. We will demonstrate flexibil-nity of our approach by analysing classical examples of SDEs with sublinearncoefficients (CIR, CEV models ).
کلیدواژه ها:
Stochastic differential equations, $theta$-Euler-Maruyama method, Convergence, CIR model.
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