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## Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence

ESAIM: PS, 12 (2008) 1-11

## Fair valuation of mortgage insurance under stochastic default and interest rates

Yang-Che Wu, Yi-Ting Huang, Shih-Kuei Lin and Ming-Che Chuang
The North American Journal of Economics and Finance 42 433 (2017)
DOI: 10.1016/j.najef.2017.08.003

## A Comparison of Biased Simulation Schemes for Stochastic Volatility Models

Roger Lord, Remmert Koekkoek and Dick J. C. van Dijk
SSRN Electronic Journal (2008)
DOI: 10.2139/ssrn.903116

## A comparison of biased simulation schemes for stochastic volatility models

Roger Lord, Remmert Koekkoek and Dick Van Dijk
Quantitative Finance 10 (2) 177 (2010)
DOI: 10.1080/14697680802392496

## The rate of convergence of the Euler scheme to the solution of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion

Yuliya S. Mishura and Svitlana V. Posashkova
Random Operators and Stochastic Equations 19 (1) 63 (2011)
DOI: 10.1515/ROSE.2011.003

## Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model Using Malliavin Integration by Parts

Martin Altmayer and Andreas Neuenkirch
SIAM Journal on Financial Mathematics 6 (1) 22 (2015)
DOI: 10.1137/130933629

## An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients

Jean-François Chassagneux, Antoine Jacquier and Ivo Mihaylov
SIAM Journal on Financial Mathematics 7 (1) 993 (2016)
DOI: 10.1137/15M1017788

## Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

Aurélien Alfonsi
Statistics & Probability Letters 83 (2) 602 (2013)
DOI: 10.1016/j.spl.2012.10.034

## A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients

István Gyöngy and Miklós Rásonyi
Stochastic Processes and their Applications 121 (10) 2189 (2011)
DOI: 10.1016/j.spa.2011.06.008

## First order strong approximations of scalar SDEs defined in a domain

Andreas Neuenkirch and Lukasz Szpruch
Numerische Mathematik 128 (1) 103 (2014)
DOI: 10.1007/s00211-014-0606-4

## Low-bias simulation scheme for the Heston model by Inverse Gaussian approximation

S. T. Tse and Justin W. L. Wan
Quantitative Finance 13 (6) 919 (2013)
DOI: 10.1080/14697688.2012.696678

## Rate of convergence in the Euler scheme for stochastic differential equations with non-Lipschitz diffusion and Poisson measure

V. P. Zubchenko and Yu. S. Mishura
Ukrainian Mathematical Journal 63 (1) 49 (2011)
DOI: 10.1007/s11253-011-0487-y

## Exact Scenario Simulation for Selected Multi-Dimensional Stochastic Processes

Eckhard Platen and Renatak Rendek
SSRN Electronic Journal (2009)
DOI: 10.2139/ssrn.2172581

## Gamma expansion of the Heston stochastic volatility model

Paul Glasserman and Kyoung-Kuk Kim
Finance and Stochastics 15 (2) 267 (2011)
DOI: 10.1007/s00780-009-0115-y

## Gamma Expansion of the Heston Stochastic Volatility Model

Paul Glasserman and Kyoung-Kuk Kim
SSRN Electronic Journal (2008)
DOI: 10.2139/ssrn.1279850

## High Order Discretization Schemes for Stochastic Volatility Models

Mohamed Sbai and Benjamin Jourdain
SSRN Electronic Journal (2011)
DOI: 10.2139/ssrn.1452727

## Efficient Simulation of the Double Heston Model

Pierre Gauthier and Dylan Possamai
SSRN Electronic Journal (2010)
DOI: 10.2139/ssrn.1434853

## A Simple Discretization Scheme for Nonnegative Diffusion Processes, with Applications to Option Pricing

Chantal Labbé, Bruno Remillard and Jean-Francois Renaud
SSRN Electronic Journal (2010)
DOI: 10.2139/ssrn.1619989

## Low-Bias Simulation Scheme for the Heston Model by Inverse Gaussian Approximation

Shu Tong Tse and Justin W. L. Wan
SSRN Electronic Journal (2010)
DOI: 10.2139/ssrn.1644977

## A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models

Xu Yang and Xiaojie Wang
Numerical Algorithms 74 (1) 39 (2017)
DOI: 10.1007/s11075-016-0137-4

## Backward simulation methods for pricing American options under the CIR process

Wenbin Hu and Junzi Zhou
Quantitative Finance 17 (11) 1683 (2017)
DOI: 10.1080/14697688.2017.1307513

## FPGA Based Accelerators for Financial Applications

Steffen Omland, Mario Hefter, Klaus Ritter, et al.
FPGA Based Accelerators for Financial Applications 191 (2015)
DOI: 10.1007/978-3-319-15407-7_9

## Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-α method

Saswati Dana and Soumyendu Raha
Journal of Computational Physics 230 (24) 8813 (2011)
DOI: 10.1016/j.jcp.2011.07.032

## Strong convergence of the stopped Euler–Maruyama method for nonlinear stochastic differential equations

Wei Liu and Xuerong Mao
Applied Mathematics and Computation 223 389 (2013)
DOI: 10.1016/j.amc.2013.08.023

## Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients

Xuerong Mao and Lukasz Szpruch
Stochastics 85 (1) 144 (2013)
DOI: 10.1080/17442508.2011.651213

## Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions

Stefano De Marco
The Annals of Applied Probability 21 (4) (2011)
DOI: 10.1214/10-AAP717

## A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

C. E. Dangerfield, D. Kay, S. MacNamara and K. Burrage
BIT Numerical Mathematics 52 (2) 283 (2012)
DOI: 10.1007/s10543-011-0351-3

## Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

Martin Hutzenthaler, Arnulf Jentzen and Peter E. Kloeden
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467 (2130) 1563 (2011)
DOI: 10.1098/rspa.2010.0348

## A backward Monte Carlo approach to exotic option pricing

G. BORMETTI, G. CALLEGARO, G. LIVIERI and A. PALLAVICINI
European Journal of Applied Mathematics 29 (1) 146 (2018)
DOI: 10.1017/S0956792517000079

## Strong rate of tamed Euler–Maruyama approximation for stochastic differential equations with Hölder continuous diffusion coefficient

Hoang-Long Ngo and Duc-Trong Luong
Brazilian Journal of Probability and Statistics 31 (1) (2017)
DOI: 10.1214/15-BJPS301

## Parameter Estimation for the Square-Root Diffusions: Ergodic and Nonergodic Cases

Mohamed Ben Alaya and Ahmed Kebaier
Stochastic Models 28 (4) 609 (2012)
DOI: 10.1080/15326349.2012.726042

## Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges

J Szavits-Nossan and M R Evans
Journal of Statistical Mechanics: Theory and Experiment 2015 (12) P12008 (2015)
DOI: 10.1088/1742-5468/2015/12/P12008

## CHI-SQUARE SIMULATION OF THE CIR PROCESS AND THE HESTON MODEL

SIMON J. A. MALHAM and ANKE WIESE
International Journal of Theoretical and Applied Finance 16 (03) 1350014 (2013)
DOI: 10.1142/S0219024913500143

## On non-polynomial lower error bounds for adaptive strong approximation of SDEs

Larisa Yaroslavtseva
Journal of Complexity 42 1 (2017)
DOI: 10.1016/j.jco.2017.04.002

## Stochastic differential equations driven by fractional Brownian motion with locally Lipschitz drift and their implicit Euler approximation

Shao-Qin Zhang and Chenggui Yuan
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 151 (4) 1278 (2021)
DOI: 10.1017/prm.2020.60

## A stochastic model for cell adhesion to the vascular wall

Christèle Etchegaray and Nicolas Meunier
Journal of Mathematical Biology 79 (5) 1665 (2019)
DOI: 10.1007/s00285-019-01407-7

## An explicit and positivity preserving numerical scheme for the mean reverting CEV model

Nikolaos Halidias
Japan Journal of Industrial and Applied Mathematics 32 (2) 545 (2015)
DOI: 10.1007/s13160-015-0183-7

## Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model

Mátyás Barczy, Mohamed Ben Alaya, Ahmed Kebaier and Gyula Pap
Journal of Statistical Planning and Inference 198 139 (2019)
DOI: 10.1016/j.jspi.2018.02.002

## STRONG CONVERGENCE FOR EULER–MARUYAMA AND MILSTEIN SCHEMES WITH ASYMPTOTIC METHOD

International Journal of Theoretical and Applied Finance 17 (02) 1450014 (2014)
DOI: 10.1142/S0219024914500149

## An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process

Steffen Dereich, Andreas Neuenkirch and Lukasz Szpruch
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468 (2140) 1105 (2012)
DOI: 10.1098/rspa.2011.0505

## Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations

Yulian Yi, Yaozhong Hu and Jingjun Zhao
Communications in Nonlinear Science and Numerical Simulation 101 105895 (2021)
DOI: 10.1016/j.cnsns.2021.105895

## Exponential integrability properties of Euler discretization schemes for the Cox--Ingersoll--Ross process

Andrei Cozma and Christoph Reisinger
Discrete and Continuous Dynamical Systems - Series B 21 (10) 3359 (2016)
DOI: 10.3934/dcdsb.2016101

## Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients

Xuerong Mao and Lukasz Szpruch
Journal of Computational and Applied Mathematics 238 14 (2013)
DOI: 10.1016/j.cam.2012.08.015

## On sub-polynomial lower error bounds for quadrature of SDEs with bounded smooth coefficients

Larisa Yaroslavtseva and Thomas Müller-Gronbach
Stochastic Analysis and Applications 35 (3) 423 (2017)
DOI: 10.1080/07362994.2016.1263157

## A note on strong approximation of SDEs with smooth coefficients that have at most linearly growing derivatives

Thomas Müller-Gronbach and Larisa Yaroslavtseva
Journal of Mathematical Analysis and Applications 467 (2) 1013 (2018)
DOI: 10.1016/j.jmaa.2018.07.041

## Tamed Euler–Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients

Hoang Long Ngo and Duc Trong Luong
Statistics & Probability Letters 145 133 (2019)
DOI: 10.1016/j.spl.2018.09.006

## Non-Negativity Preserving Numerical Algorithms for Problems in Mathematical Finance

Yuan Yuan
Applied Mathematics 09 (03) 313 (2018)
DOI: 10.4236/am.2018.93024

## Convergence of an Euler Scheme for a Hybrid Stochastic-Local Volatility Model with Stochastic Rates in Foreign Exchange Markets

Andrei Cozma, Matthieu Mariapragassam and Christoph Reisinger
SIAM Journal on Financial Mathematics 9 (1) 127 (2018)
DOI: 10.1137/17M1114569

## Strong Convergence Rates for Euler Approximations to a Class of Stochastic Path-Dependent Volatility Models

Andrei Cozma and Christoph Reisinger
SIAM Journal on Numerical Analysis 56 (6) 3430 (2018)
DOI: 10.1137/17M1136754

## On arbitrarily slow convergence rates for strong numerical approximations of Cox–Ingersoll–Ross processes and squared Bessel processes

Mario Hefter and Arnulf Jentzen
Finance and Stochastics 23 (1) 139 (2019)
DOI: 10.1007/s00780-018-0375-5

## Strong order 1/2 convergence of full truncation Euler approximations to the Cox–Ingersoll–Ross process

Andrei Cozma and Christoph Reisinger
IMA Journal of Numerical Analysis (2018)
DOI: 10.1093/imanum/dry067

## Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

Lukasz Szpruch, Xuerong Mao, Desmond J. Higham and Jiazhu Pan
BIT Numerical Mathematics 51 (2) 405 (2011)
DOI: 10.1007/s10543-010-0288-y

## Predictive Systems Under Economic Constraints

Maxime Bonelli and Daniel Mantilla-Garcia
SSRN Electronic Journal (2014)
DOI: 10.2139/ssrn.2441323

## Least-Squares Estimation for the Subcritical Heston Model Based on Continuous-Time Observations

Mátyás Barczy, Balázs Nyul and Gyula Pap
Journal of Statistical Theory and Practice 13 (1) (2019)
DOI: 10.1007/s42519-018-0007-6

## Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion

Jialin Hong, Chuying Huang, Minoo Kamrani and Xu Wang
Stochastic Processes and their Applications 130 (5) 2675 (2020)
DOI: 10.1016/j.spa.2019.07.014

## Convergence rate of Euler scheme for time-inhomogeneous SDEs involving the local time of the unknown process

Mohamed Bourza and Mohsine Benabdallah
Stochastic Models 36 (3) 452 (2020)
DOI: 10.1080/15326349.2020.1748506

## On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case

Libo Li and Dai Taguchi
BIT Numerical Mathematics 59 (3) 747 (2019)
DOI: 10.1007/s10543-019-00753-8

## Approximation of the distribution of a stationary Markov process with application to option pricing

Gilles Pagès and Fabien Panloup
Bernoulli 15 (1) (2009)
DOI: 10.3150/08-BEJ142

## Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process

Mohsine Benabdallah, Youssfi Elkettani and Kamal Hiderah
Monte Carlo Methods and Applications 22 (4) (2016)
DOI: 10.1515/mcma-2016-0115

## Local asymptotic properties for Cox‐Ingersoll‐Ross process with discrete observations

Mohamed Ben Alaya, Ahmed Kebaier and Ngoc Khue Tran
Scandinavian Journal of Statistics 47 (4) 1401 (2020)
DOI: 10.1111/sjos.12494

## Ergodic approximation of the distribution of a stationary diffusion: Rate of convergence

Gilles Pagès and Fabien Panloup
The Annals of Applied Probability 22 (3) (2012)
DOI: 10.1214/11-AAP779

## Series Expansions and Direct Inversion for the Heston Model

Simon J. A. Malham, Jiaqi Shen and Anke Wiese
SIAM Journal on Financial Mathematics 12 (1) 487 (2021)
DOI: 10.1137/19M126791X

## Strong convergence of the symmetrized Milstein scheme for some CEV-like SDEs

Mireille Bossy and Héctor Olivero
Bernoulli 24 (3) (2018)
DOI: 10.3150/16-BEJ918

## Realised volatility and parametric estimation of Heston SDEs

Robert Azencott, Peng Ren and Ilya Timofeyev
Finance and Stochastics 24 (3) 723 (2020)
DOI: 10.1007/s00780-020-00427-2

## Simulation of Non-Lipschitz Stochastic Differential Equations Driven by $\alpha$-Stable Noise: A Method Based on Deterministic Homogenization

Georg A. Gottwald and Ian Melbourne
Multiscale Modeling & Simulation 19 (2) 665 (2021)
DOI: 10.1137/20M1333183

## Key Technique of Almost Exact Simulation for Non-affine Heston Model

Xingyin Liang, Youfa Sun and Yuhang Yao
Journal of Physics: Conference Series 1624 (2) 022016 (2020)
DOI: 10.1088/1742-6596/1624/2/022016

## The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes

Raphael Naryongo, Philip Ngare, Anthony Waititu and Remi Léandre
International Journal of Mathematics and Mathematical Sciences 2021 1 (2021)
DOI: 10.1155/2021/4050722

## Convergence and stability of modified partially truncated Euler–Maruyama method for nonlinear stochastic differential equations with Hölder continuous diffusion coefficient

Hongfu Yang and Jianhua Huang
Journal of Computational and Applied Mathematics 404 113895 (2022)
DOI: 10.1016/j.cam.2021.113895

## The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model

Cónall Kelly, Gabriel Lord and Heru Maulana
Journal of Computational and Applied Mathematics 114208 (2022)
DOI: 10.1016/j.cam.2022.114208

## Strong convergence rates for Cox–Ingersoll–Ross processes — Full parameter range

Mario Hefter and André Herzwurm
Journal of Mathematical Analysis and Applications 459 (2) 1079 (2018)
DOI: 10.1016/j.jmaa.2017.10.076

## Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations

Nan Chen and Zhengyu Huang
Mathematics of Operations Research 38 (3) 591 (2013)
DOI: 10.1287/moor.2013.0585

## The truncated Euler–Maruyama method for CIR model driven by fractional Brownian motion

Xiangyu Gao, Jianqiao Wang, Yanxia Wang and Hongfu Yang
Statistics & Probability Letters 189 109573 (2022)
DOI: 10.1016/j.spl.2022.109573