Consider the continuous dynamical system
$$\alpha\ddot{S}+\dot{S}=\mathcal{F}(S,t),$$
such that $\alpha\in\mathbb{R}$ and $\mathcal{F}$ is real and analytic. We assume that if a solution for $S$ exists, then $S$ is deterministic. However, for a sufficiently high maximal Lyapunov exponent $\lambda$, when $$\frac{1}{\lambda}\ln\left(\frac{a}{\lVert\delta_0\rVert}\right)\leq\min T,$$
$a$ is the tolerance of prediction, and the initial parameters are uncertain to within $\lVert\delta_0\rVert$ from the true initial conditions, does the system permit no-arbitrage for underlying asset price $S$? If not, does a risk-neutral measure / no free lunch with vanishing risk exist. I would be grateful for any help or pointers to relevant literature.
