Yes, and El-Erian certainly understands that. He was using classes of analytic functions as a relatively simple example of things that had the properties he wa

Yes, and El-Erian certainly understands that. He was using classes of analytic functions as a relatively simple example of things that had the properties he was talking about. Generally speaking in finance things like price trajectories and timeseries like economic indicators are modelled as stochastic processes. Often a Wiener process with drift, and then jumps and jumps in volatility added as needed to capture the dynamics of the situation if required. So there's definitely no requirement to be smooth or diferentiable everywhere, and there is even less requirement for a positive 2nd derivative to lead to a positive slope/turnaround.