| Abstract: |
| The Nobel Prize winning Black-Scholes equation for stock options and the heat equation are both model equations of the generalized problem
\[
\frac{\partial u}{\partial t}=P_2(A_a)u,
\]
where $P_2(z)=\alpha z^2+ \beta z+\gamma$ is a quadratic polynomial with $\alpha > 0$
and $A_a = x^a\frac{\partial}{\partial x}$ is an operator for functions on
$[0,\infty) \times [0,\infty)$ with $0\le a \le 1$.
For each operator $A_a$ the corresponding degenerate parabolic equation is governed by a semigroup of operators which is chaotic on a suitable class of Banach spaces; thus, we unify, simplify and significantly extend
earlier results obtained by H. Emamirad, G. R. Goldstein and J. A. Goldstein for the Black-Scholes equation ($a=1$) and the heat equation ($a=0$).
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Joint work with G. Ruiz Goldstein, J. A. Goldstein and S. Romanelli.
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Supported by MUR-PNRR project code CN00000013 `\emph{National Centre for HPC, Big Data and Quantum Computing}` - Spoke 10 `\emph{Quantum Computing}`. |
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