Narrow Results

Self-Organized Criticality (SOC) phenomena could have a significant effect on the dynamics of ecosystems. The Bak–Sneppen (BS) model is a simple and robust model of biological evolution that exhibits punctuated equilibrium behavior. Here, we will introduce random version of BS model. We also generalize the single objective BS model to a multiobjective one.

This chapter extends the Margrabe formula such that it is suitable for accounting for any type jump of stocks. Despite the fact that prices of an exchange option are characterized by jumps, it seems no study has explored those price jumps of an exchange option. The jump in this chapter is illustrated by a Poisson process. Moreover, the Poisson process can be extended into Cox process in case there is more than one jump. The results illustrate that incompleteness in an exchange option leads to a premium which in turn increases an option value whilst hedging strategies reveal mixed-bag type of results.