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Keywords = nonstandard Volterra integral equations

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12 pages, 298 KiB  
Article
An Alternative Numerical Scheme to Approximate the Early Exercise Boundary of American Options
by Denis Veliu, Roberto De Marchis, Mario Marino and Antonio Luciano Martire
Mathematics 2023, 11(1), 187; https://doi.org/10.3390/math11010187 - 29 Dec 2022
Viewed by 1929
Abstract
This paper deals with a new numerical method for the approximation of the early exercise boundary in the American option pricing problem. In more detail, using the mean-value theorem for integrals, we provide a flexible algorithm that allows for reaching a more accurate [...] Read more.
This paper deals with a new numerical method for the approximation of the early exercise boundary in the American option pricing problem. In more detail, using the mean-value theorem for integrals, we provide a flexible algorithm that allows for reaching a more accurate numerical solution with fewer calculations rather than other previously described methods. Full article
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13 pages, 1178 KiB  
Article
Integrable Deformations and Dynamical Properties of Systems with Constant Population
by Cristian Lăzureanu
Mathematics 2021, 9(12), 1378; https://doi.org/10.3390/math9121378 - 14 Jun 2021
Cited by 1 | Viewed by 1866
Abstract
In this paper we consider systems of three autonomous first-order differential equations x˙=f(x),x=(x,y,z),f=(f1,f2,f3) such [...] Read more.
In this paper we consider systems of three autonomous first-order differential equations x˙=f(x),x=(x,y,z),f=(f1,f2,f3) such that x(t)+y(t)+z(t) is constant for all t. We present some Hamilton–Poisson formulations and integrable deformations. We also analyze the case of Kolmogorov systems. We study from some standard and nonstandard Poisson geometry points of view the three-dimensional Lotka–Volterra system with constant population. Full article
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