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.

Publication Title

Proceedings of the American Mathematical Society