A Mathematical Nuance that Profoundly Affects Economics
Vortrag von Prof. Dr. Philip Protter Datum: 18.10.13 Zeit: 16.00 - 16.50 Raum: Y27H46
The role of martingales in Mathematical Finance is basic and fundamental. Yet to make the mathematical models work well, it is necessary to use a slight extension of martingales to local martingales, and occasionally even to sigma martingales. The difference between a martingale and a strict local martingale (ie, a local martingale that is not a martingale) is so slight that it is hard to detect from data. Yet when a price or a wealth process is a strict local martingale, the phenomenon reflects problematic behavior of the financial markets. Absent mathematical models, this behavior can go unnoticed until its consequences are severe. We will discuss several examples of this pathology. These examples indicate that it might be more common than is typically believed.