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We derive an optimal strategy for minimizing the expected loss in the two-period economy when a pivotal decision needs to be made during the first time period and cannot be subsequently reversed. Our interest in the problem has been motivated by the classical shoppers dilemma during the Black Friday promotion period, and our solution crucially relies on the pioneering work of McDonnell and Abbott on the two-envelope paradox.
Different people have different habits of describing their intents in conversations. Some people may tend to deliberate their full intents in several successive utterances, i.e., they use several consistent messages for readability instead of a long
In this paper, we investigate the cooling-off effect (opposite to the magnet effect) from two aspects. Firstly, from the viewpoint of dynamics, we study the existence of the cooling-off effect by following the dynamical evolution of some financial va
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a n
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem using singul
Understanding the statistical properties of recurrence intervals of extreme events is crucial to risk assessment and management of complex systems. The probability distributions and correlations of recurrence intervals for many systems have been exte