Integer constraints in mathematical finance

The hedging of derivatives, which manages the risk of certain financial contracts, is one of the most successful areas of applying mathematical finance. Any model employed for this task simplifies reality, in order to make the complexity of financial markets tractable. In particular, models in current use allow to divide any asset into arbitrary small pieces. This leads to theoretical trading strategies that cannot be implemented in practice. In this project, the inherent integrality of actual trading portfolios will be analyzed from various perspectives. We will investigate the hedge error that results from hedging derivatives with integral, instead of real-valued, strategies. For large amounts of identical options, as are commonly sold by investment banks, scaling effects will reduce this error, but so far there is no research on this. Furthermore, we will study the trading volume resulting from hedging. By classical approaches, which use stochastic processes of infinite variation, this problem cannot be answered. Finally, we will study options on commodity futures. Here, the underlyings granularity can be significant, such as multiples of 1000 barrels of crude oil. Again, we will analyze how many options are needed to make the effect of integer constraints manageable.