Some optimal variance stopping problems revisited with an application to the Italian Ftse-Mib stock index

Optimal variance stopping (O.V.S.) problems are a new class of optimal stopping problems that differ from the classical ones because of their non linear (quadratic) dependence on the expectation operator. These problems were introduced by Pedersen (2011), who provided an effective solution method and derived the explicit solutions to the O.V.S. problem for some important examples of diffusion processes. In this article, we analyze the examples of Pedersen (2011) in light of the results in Buonaguidi (2015), where an alternative method for solving an O.V.S. problem was developed: this method is based on the solution of a constrained optimal stopping problem, whose maximization, over all the admissible constraints, returns the solution to the O.V.S. problem. Using real data on the Italian Ftse-Mib stock index, we also discuss how the solution to the O.V.S. problem for a geometric Brownian motion can be used in trading strategies.