Markets with random lifetimes and private values: mean reversion and option to trade

We consider a market in which traders arrive at random times, with random private values for the single-traded asset. A trader’s optimal trading decision is formulated in terms of exercising the option to trade one unit of the asset at the optimal stopping time. We solve the optimal stopping problem under the assumption that the market price follows a mean-reverting diffusion process. The model is calibrated to experimental data taken from Alton and Plott (Principles of continuous price determination in an experimental environment with flows of random arrivals and departures. Working paper, Caltech, 2010 ), resulting in a very good fit. In particular, the estimated long-term mean of the traded prices is close to the theoretical long-term mean at which the expected number of buys is equal to the expected number of sells. We call that value long-term competitive equilibrium, extending the concept of flow competitive equilibrium of Alton and Plott (Principles of continuous price determination in an experimental environment with flows of random arrivals and departures. Working paper, Caltech, 2010 ). Copyright Springer-Verlag Italia 2015