Central tenets of modern portfolio theory suggest homogeneity of optimal strategies and turnpike theorems. In contrast with these common
beliefs, the findings of the recent paper "Young, Timid, and Risk Takers" (Paolo Guasoni, Lóránt Nagy, Miklós Rásonyi) show that, in the regime of high risk aversion (i.e. exponential utility), the classical view is not at all universal.

Our framework figures a price process that follows a drifted diffusion that is a generalization of the well-known Ornstein-Uhlenbeck process, more precisely a nonlinear "power model" version of it.

Heuristic reasoning based on a model with discrete autoregressive price shows that, rather suprisingly, the limiting Ornstein-Uhlenbeck model displays an optimal growth of the certainty equivalent which is quadratic in the time horizon.

This result extends to the power model, with the growth rate depending on the strength of the nonlinearity in the mean reverting drift. Asymptotically optimal strategies exploit both dependence on the time horizon and the mean reversion of the price. Despite the ergodicity of the underlying model, the strategies do not converge in the limit.
Speaker(s): Lorant Nagy (Alfred Renyi Institute)