Explicit Computations for Delayed Semistatic Hedging

In this work we consider the exponential utility maximization problem in the framework of semistatic hedging. In addition to the usual setting considered in mathematical finance, we also consider an investor who is informed about the risky asset's price changes with a delay. When the stock increments are independent, identically distributed, and follow a normal distribution, we compute explicitly the value of the problem and the corresponding optimal hedging strategy in a discrete- and a continuous-time setting. In discrete time, our approach is based on duality theory and tools from linear algebra which are related to banded matrices and Toeplitz matrices. Next, we study an analogous continuous-time model where it is possible to trade at fixed equally spaced times. In this model, we compute the scaling limit for both the trading strategy and the achieved value as the frequency of the trading events increases. Finally, we prove that this scaling limit coincides with the continuous-time hedging problem.