Events
Department of Mathematics and Statistics
Texas Tech University
 | Wednesday
Nov. 2
|
| Algebra and Number Theory
No Seminar
|
This talk discusses computing the Morse index for a free boundary minimal submanifold for
more specific problems. We focused on the corresponding problem with fixed boundary conditions
and the association with the Dirichlet-to-Neumann map to Jacobi fields. Also, we will discuss an
application of it.
Watch online via this Zoom link.
Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing.
As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe
occurrences and interest rates in a sufficiently flexible and statistically reliable way within a
unifying asset pricing framework.
Consequently, little is known empirically about the expected risk-premia of CAT bonds.
The primary contribution of this paper is to present a unified Bayesian CAT bond pricing framework
based on uncertainty quantification of catastrophes and interest rates.
Our framework allows for complex beliefs about catastrophe risks to capture the distinct and common
patterns in catastrophe occurrences, and when combined with stochastic interest rates, yields a
unified asset pricing approach with informative expected risk premia.
Specifically, using a modified collective risk model -- Dirichlet Prior-Hierarchical Bayesian Collective
Risk Model (DP-HBCRM) framework -- we model catastrophe risk via a model-based clustering approach.
Interest rate risk is modeled as a CIR process under the Bayesian approach.
As a consequence of casting CAT pricing models into our framework,
we evaluate the price and expected risk premia of various CAT bond contracts corresponding to
clustering of catastrophe risk profiles.
Numerical experiments show how these clusters reveal how CAT bond prices and expected risk premia
relate to claim frequency and loss severity.
This is joint work with Dixon Domfeh and Arpita Chatterjee.