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TITLE: What risks lead to ruin?
SPEAKER: Venkat Anantharam (UC Berkeley)
DATE: 2:00 - 3:00 PM, Wednesday, October 24, 2012
LOCATION: Eureka, 1U
ABSTRACT:
Insurance transfers losses associated with risks to the insurer for a
price, the premium. We adopt the collective risk approach. Namely, we
abstract the problem to include just two agents: the insured and the
insurer. We are interested in scenarios where the underlying model for
the loss distribution is not very well known, and the potential losses
can also be quite high. One modern scenario of particular interest
that fits in this framework is the question of how to insure potential
losses incurred by entities operating on the Internet. In the absence
of enough data to build reasonable parametric loss models, it is
natural to adopt a nonparametric formulation. Considering a natural
probabilistic framework for the insurance problem, assuming
independent and identically distributed (i.i.d.) losses, we derive a
necessary and sufficient condition on nonparametric loss models such
that the insurer remains solvent despite the losses taken on.
In more detail, we model the loss at each time by a nonnegative
integer. An insurer's scheme is defined by the premium demanded by the
insurer from the insured at each time as a function of the loss
sequence observed up to that time. The insurer is allowed to wait for
some period before beginning to insure the process, but once insurance
commences, the insurer is committed to continue insuring the
process. All that the insurer knows is that the loss sequence is a
realization from some i.i.d. process with marginal law in some set of
probability distributions on the nonnegative integers. The insurer
does not know which distribution in this set of distributions
describes the marginal distribution of the loss sequence. The insurer
goes bankrupt when the loss incurred exceeds the built up buffer of
reserves from premiums charged so far. 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.
(Joint work with Narayana Prasad Santhanam, University of Hawaii.)
BIOGRAPHY:
Venkat Anantharam has been with the Electrical Engineering and
Computer Science Department, University of California, Berkeley since
1994 and is now a Professor. 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, 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 corecipient of the 1998 Prize
Paper Award of the IEEE Information Theory Society, and a corecipient
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.
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