The Value of Informational Arbitrage

In the context of a general semimartingale model, we aim at answering the following question: How much is an investor willing to pay for learning some inside information that allows to achieve arbitrage? If such a value exists, we call it the value of informational arbitrage. In particular, we are interested in the case where the inside information yields arbitrage opportunities but not unbounded profits with bounded risk. In the spirit of Amendinger et al. (2003), we provide a general answer to this question by means of an indifference valuation approach. To this effect, we establish some new results on models with additional information and study optimal investment-consumption problems in the presence of additional information and arbitrage, also allowing for the possibility of leverage. We characterize when the value of informational arbitrage is universal, in the sense that it does not depend on the preference structure. This talk is based on joint work with H.N. Chau and A. Cosso.