On measures of unfairness and an optimal currency transaction tax

The purpose of the present paper is the analysis of a model describing how herd behaviour and self-fulfilling prophecies can influence currency exchange rates, and what the impact of a currency transaction tax would be. These considerations yield a stochastic differential equation that can be studied using the methods of infinitesimal analysis. We will show, using a suitable notion of unfairness for discounted price processes which measures the distance from being a martingale, that the fairest tax rate is the maximal one subject to the condition that it does not affect real-economic speculation.