OPTIMAL SWITCHING UNDER COMPETITION: A DISCRETE-TIME OPTIMAL STOPPING APPROACH

Abstract

Motivated by markets in which new entrants challenge established monopolies, we study the problem of determining an optimal switching time for consumers facing competing stochastic price dynamics. In the particular case of the sequences of prices—or premiums—being sub-martingales, an optimal stopping time is described by a simple relation between the increasing processes of the Doob decompositions of these sub-martingales. We present a statistical methodology allowing the application of the results including a Bayesian approach for the case of scarce data. We present a simulation study in the case of average linear growth of the prices increments and we develop two efficient estimation procedures of the parameters of these models allowing accurate estimation of the optimal stopping time. In the particular cases presented, the simulated smallest optimal stopping time coincides with the optimal stopping time studied.