Quantifying Risks of Extremes

• Activity Number: 79
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Ugur Alparslan*+
• Companies: American University
• Keywords: Stable ; Risk ; Extreme ; Ruin

Abstract

We study "ruin probability," a commonly used performance measure in actuarial science, as a risk assessment tool for extreme events. Classical ruin problem usually assumes independent, identically distributed steps and a linear drift. However a more realistic setting in the context of climate extremes requires temporal dependence in a given variable. Moreover, empirical evidence showing increased likelihood of extremes necessitates modeling these variables using heavy tailed probability laws. The case of heavy tailed, dependent steps is also interesting from a purely mathematical point of view as it raises the possibility of relating the dependence structure of heavy tailed stochastic processes to the asymptotic behavior of the ruin probability. This becomes particularly intriguing when the variables are highly volatile so that it is not possible to use traditional covariance based measures to quantify the dependence structure of the process. We propose a probability model, which uses dependent variables following infinite-variance stable distributions, and allows for nonlinear drifts. We then analyze the effects of range of dependence on the ruin probability in this setting.