Abstract
A motivation for studying the nonlinear Black- Scholes equation with a nonlinear volatility arises from option pricing models taking into account e.g. nontrivial transaction costs, investor’s preferences, feedback and illiquid markets effects and risk from a volatile (unprotected) portfolio. In this work we develop positivity preserving algorithm for solving a large class of non-linear models in mathematical finance on the original (infinite) domain. Numerical examples are discussed.
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Koleva, M.N. (2013). Positivity Preserving Numerical Method for Non-linear Black-Scholes Models. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_40
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DOI: https://doi.org/10.1007/978-3-642-41515-9_40
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