What Risks Lead to Ruin?
Professor Venkat Anantharam
Insurance transfers losses from the insuree to the insurer for a price per unit time, the premium. The pace of modern technology throws up scenarios where it is difficult to have confidence about what the loss distribution is. For instance, how would one insure potential losses incurred by entities operating on the Internet? Nevertheless, insurance has many benefits: by aggregating risk, it allows for more risk-taking by innovators. The availability of insurance can thus be viewed indirectly as a driver of technological advances.
To address how to properly insure poorly modeled risks, it is natural to adopt a nonparametric formulation. We may assume that all that the insurer knows (or believes) is that the loss sequence is a realization from some family of loss distributions characterized in a simple qualitative way. For instance, the insurer may just assume that bigger losses are less likely than smaller losses. The insurer will go bankrupt if the loss incurred exceeds the built up buffer of reserves from premiums charged so far. Can the insurer set premiums so that the probability of going bankrupt is less than any prescribed threshold irrespective of which distribution from the class is the true loss distribution ?
We show that a nonparametric loss model of this type is insurable iff it contains no “deceptive” distributions. Here the notion of “deceptive” distribution is precisely defined in information-theoretic terms. There appear to be close connections between classes of insurable probability distributions and classes of distributions studied in universal data compression.
The necessary background from information theory and risk theory will be provided during the talk. Our results are a first step in this general direction, which holds out many avenues for further development.
(Joint work with Narayana Prasad Santhanam, University of Hawaii, Manoa.)
Venkat Anantharam is a Professor in the Department of Electrical Engineering and Computer Sciences at the University of California at Berkeley. He received the B.Tech. degree in electronics in 1980 from the Indian Institute of Technology, Madras (IIT-M), and the M.A. and C.Phil. degrees in mathematics and the M.S. and Ph.D. degrees in electrical engineering in 1983, 1984, 1982, and 1986, respectively, all from the University of California, Berkeley. From 1986 to 1994, he was on the faculty of the School of Electrical Engineering at Cornell University, Ithaca, NY. Dr. Anantharam received the Philips India Medal and the President of India Gold Medal from IIT-M in 1980, and an NSF Presidential Young Investigator award (1988-1993). He is a co-recipient of the 1998 Prize Paper Award of the IEEE Information Theory Society, and a co-recipient of the 2000 Stephen O. Rice Prize Paper Award of the IEEE Communications Theory Society. He received the Distinguished Alumnus Award from IIT-M in 2008.