The multivariate lack-of-memory property: Analytical characterizations and applications to mathematical finance

OMI Seminar Series

Characterized by the lack-of-memory property, the exponential and the geometric law have a prominent role in reliability theory, queuing theory, and mathematical finance. If this defining property is meaningfully lifted to the multivariate case, the resulting multivariate equivalent is the Marshall-Olkin exponential law and the wide-sense geometric distribution. Both distributions have appealing statistical properties for applications in portfolio-credit risk and insurance.

However, both distributions are parameterized by O(2^d) parameters in dimension d, exposing us to massive numerical difficulties in real-world portfolio sizes. To overcome these problems, we identify the subclasses with conditionally iid components and show how these can be constructed as one-factor models and extended to multi-factor models; the factors being Lévy subordinators and discrete random walks, respectively. On a theoretical level, this reveals interesting mathematical connections to (log-)completely monotone sequences and moment problems. On a practical level, we use the Lévy-frailty model as our base case for the construction of interesting portfolio default models.

Joint work with Jan-Frederik Mai and Natalia Shenkman.


Matthias Scherer (TUM)

Tuesday, November 13, 2012 - 14:15
to 15:15