The investment boundaries defined by Grenadier (2002) for an oligopoly investment game determine equilibria in open-loop strategies. As closed-loop strategies, they are not equilibria, because any firm by investing sooner can preempt the investments of other firms and expropriate the growth...

The investment boundaries defined by Grenadier (2002) for an oligopoly investment game determine equilibria in open-loop strategies. As closed-loop strategies, they are not equilibria, because any firm by investing sooner can preempt the investments of other firms and expropriate the growth...

This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and...

When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise fit and estimation error. We then show...