Chaotic solution for the Black-Scholes equation
The Black-Scholes semigroup is studied on spaces of continuous functions on (0,∞) which may grow at both 0 and at ∞, which is important since the standard initial value is an unbounded function. We prove that in the Banach spaces with norm, the Black-Scholes semigroup is strongly continuous and chaotic for s > 1, τ ≥ 0 with sν > 1, where √2ν is the volatility. The proof relies on the Godefroy-Shapiro hypercyclicity criterion. © 2011 American Mathematical Society.
Proceedings of the American Mathematical Society
Emamirad, H., Goldstein, G., & Goldstein, J. (2012). Chaotic solution for the Black-Scholes equation. Proceedings of the American Mathematical Society, 140 (6), 2043-2052. https://doi.org/10.1090/S0002-9939-2011-11069-4