Well-Posedness Analysis of Leland's Nonlinear Black-Scholes Equation with Transaction Costs

Well-Posedness Analysis of Leland's Nonlinear Black-Scholes Equation with Transaction Costs | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 February 2026 V1 Latest version Share on Well-Posedness Analysis of Leland's Nonlinear Black-Scholes Equation with Transaction Costs Authors : Taimas Assan 0009-0000-5386-2171 [email protected] , Shynggyskhan Kalabay , and Dongming Wei Authors Info & Affiliations https://doi.org/10.22541/au.177064759.95062621/v1 143 views 91 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper establishes the well-posedness of Leland’s nonlinear Black-Scholes equation incorporating transaction costs. The model, derived from the classical Black-Scholes framework with proportional transaction costs and discrete rebalancing assumptions, results in a nonlinear parabolic partial differential equation with nonlinear volatility. Under the condition 0 1, where Le is the Leland constant representing transaction cost intensity, we prove existence and uniqueness of weak solutions using an energy method and Galerkin approximation, based on a transformed version of the original model. Uniqueness is established via energy estimates combined with Poincaré’s inequality and Gronwall’s lemma, while existence follows from monotone operator theory and the Minty-Browder lemma applied to the Galerkin approximation scheme. The analysis confirms the mathematical robustness of Leland’s model for practical financial applications under moderate transaction cost regimes, providing a rigorous foundation for numerical implementations. Supplementary Material File (manuscript.pdf) Download 314.59 KB Information & Authors Information Version history V1 Version 1 09 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords energy estimates galerkin method leland model nonlinear black-scholes equation nonlinear parabolic pdes option pricing sobolev spaces weak solutions well-posedness analysis Authors Affiliations Taimas Assan 0009-0000-5386-2171 [email protected] Nazarbayev University View all articles by this author Shynggyskhan Kalabay Nazarbayev University View all articles by this author Dongming Wei Nazarbayev University View all articles by this author Metrics & Citations Metrics Article Usage 143 views 91 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Taimas Assan, Shynggyskhan Kalabay, Dongming Wei. Well-Posedness Analysis of Leland's Nonlinear Black-Scholes Equation with Transaction Costs. Authorea . 09 February 2026. DOI: https://doi.org/10.22541/au.177064759.95062621/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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