Abstract/Overview
We study a nonlinear Black-Scholes partial differential equation whose nonlinearity is as a result of a feedback effect. This is an illiquid market effect arising from transaction costs. An analytic solution to the nonlinear Black-Scholes equation via a solitary wave solution is currently unknown. After transforming the equation into a parabolic nonlinear porous medium equation, we find that the assumption of a traveling wave profile to the later equation reduces it to ordinary differential equations. This together with the use of localizing boundary conditions facilitate a twice continuously differentiable nontrivial analytic solution by integrating directly.
<div>Onyango, < (2024). Analytic solution of a nonlinear black-scholes partial differential equation. Afribary. Retrieved from https://track.afribary.com/works/analytic-solution-of-a-nonlinear-black-scholes-partial-differential-equation
<div>Onyango, <div>Esekon "Analytic solution of a nonlinear black-scholes partial differential equation" Afribary. Afribary, 04 Jun. 2024, https://track.afribary.com/works/analytic-solution-of-a-nonlinear-black-scholes-partial-differential-equation. Accessed 11 Jul. 2024.
<div>Onyango, <div>Esekon . "Analytic solution of a nonlinear black-scholes partial differential equation". Afribary, Afribary, 04 Jun. 2024. Web. 11 Jul. 2024. < https://track.afribary.com/works/analytic-solution-of-a-nonlinear-black-scholes-partial-differential-equation >.
<div>Onyango, <div>Esekon . "Analytic solution of a nonlinear black-scholes partial differential equation" Afribary (2024). Accessed July 11, 2024. https://track.afribary.com/works/analytic-solution-of-a-nonlinear-black-scholes-partial-differential-equation