An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process
S Dereich, A Neuenkirch… - Proceedings of the …, 2012 - royalsocietypublishing.org
We analyse the strong approximation of the Cox–Ingersoll–Ross (CIR) process in the
regime where the process does not hit zero by a positivity preserving drift-implicit Euler-type …
regime where the process does not hit zero by a positivity preserving drift-implicit Euler-type …
First order strong approximations of scalar SDEs defined in a domain
A Neuenkirch, L Szpruch - Numerische Mathematik, 2014 - Springer
We are interested in strong approximations of one-dimensional SDEs which have non-
Lipschitz coefficients and which take values in a domain. Under a set of general …
Lipschitz coefficients and which take values in a domain. Under a set of general …
Continuous time mean variance asset allocation: A time-consistent strategy
J Wang, PA Forsyth - European Journal of Operational Research, 2011 - Elsevier
We develop a numerical scheme for determining the optimal asset allocation strategy for
time-consistent, continuous time, mean variance optimization. Any type of constraint can be …
time-consistent, continuous time, mean variance optimization. Any type of constraint can be …
Positivity preserving stochastic θ-methods for selected SDEs
C Scalone - Applied Numerical Mathematics, 2022 - Elsevier
Several applications are modelled by stochastic differential equations with positive
solutions. Numerical methods, able to preserve positivity, are absolutely needed in this case …
solutions. Numerical methods, able to preserve positivity, are absolutely needed in this case …
Convergence, non-negativity and stability of a new Milstein scheme with applications to finance
We propose and analyse a new Milstein type scheme for simulating stochastic differential
equations (SDEs) with highly nonlinear coefficients. Our work is motivated by the need to …
equations (SDEs) with highly nonlinear coefficients. Our work is motivated by the need to …
Strong and weak convergence rates of logarithmic transformed truncated EM methods for SDEs with positive solutions
Z Lei, S Gan, Z Chen - Journal of Computational and Applied Mathematics, 2023 - Elsevier
To inherit numerically the positivity of stochastic differential equations (SDEs) with non-
globally Lipschitz coefficients, we devise a novel explicit method, called logarithmic …
globally Lipschitz coefficients, we devise a novel explicit method, called logarithmic …
Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations
Y Yi, Y Hu, J Zhao - Communications in Nonlinear Science and Numerical …, 2021 - Elsevier
In this paper, we propose a class of explicit positivity preserving numerical methods for
general stochastic differential equations which have positive solutions. Namely, all the …
general stochastic differential equations which have positive solutions. Namely, all the …
[HTML][HTML] Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion
I Tubikanec, M Tamborrino, P Lansky… - Journal of Computational …, 2022 - Elsevier
We provide a comparative analysis of qualitative features of different numerical methods for
the inhomogeneous geometric Brownian motion (IGBM). The limit distribution of the IGBM …
the inhomogeneous geometric Brownian motion (IGBM). The limit distribution of the IGBM …
Balanced Milstein Methods for Ordinary SDEs.
Convergence, consistency, stability and pathwise positivity of balanced Milstein methods for
numerical integration of ordinary stochastic differential equations (SDEs) are discussed. This …
numerical integration of ordinary stochastic differential equations (SDEs) are discussed. This …