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Mathematics
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Advances in Stochastic Differential Equations and Applications to Finance
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Advances in Stochastic Differential Equations and Applications to Finance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 4265

Special Issue Editor

Prof. Dr. Nikos Halidias

E-Mail Website
Guest Editor
Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos, 83200 Karlovassi, Greece
Interests: differential equation; stochastic analysis; stochastic differential equation and its application in finance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Stochastic differential equations (SDEs) are an active interdisciplinary area at the crossroads of stochastic analysis, partial differential equations, and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, superprocesses, and continuum physics are among the most interesting topics where SDEs can be applied. This Special Issue welcomes high-quality articles in fields strongly connected to SDEs, such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic partial differential equations (PDEs), numerical solution of SDEs, and applications to financial mathematics.

Prof. Dr. Nikos Halidias
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Theory of stochastic differential equations
  • Numerical solution of SDEs
  • Financial mathematics

Published Papers (2 papers)

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Research

14 pages, 462 KiB  
Article
A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps
by Yang Li, Yaolei Wang, Taitao Feng and Yifei Xin
Mathematics 2021, 9(3), 224; https://doi.org/10.3390/math9030224 - 23 Jan 2021
Cited by 2 | Viewed by 1862
Abstract
In this paper, we propose a new weak second-order numerical scheme for solving stochastic differential equations with jumps. By using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, we theoretically prove that the numerical scheme has second-order convergence rate. To demonstrate the [...] Read more.
In this paper, we propose a new weak second-order numerical scheme for solving stochastic differential equations with jumps. By using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, we theoretically prove that the numerical scheme has second-order convergence rate. To demonstrate the effectiveness and the second-order convergence rate, three numerical experiments are given. Full article
(This article belongs to the Special Issue Advances in Stochastic Differential Equations and Applications to Finance)
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15 pages, 10436 KiB  
Article
Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods
by Zhenyu Wang, Qiang Ma and Xiaohua Ding
Mathematics 2020, 8(12), 2195; https://doi.org/10.3390/math8122195 - 9 Dec 2020
Cited by 1 | Viewed by 1673
Abstract
Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that [...] Read more.
Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that the improved methods can preserve conserved quantity of the original SDEs in Stratonovich sense. In addition, in order to deal with SDEs with multiple conserved quantities, a strategy is represented so that the improved methods can preserve multiple conserved quantities. The mean-square convergence and ability to preserve conserved quantity of the proposed methods are proved. Numerical experiments are implemented to support the theoretical results. Full article
(This article belongs to the Special Issue Advances in Stochastic Differential Equations and Applications to Finance)
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