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UID:www.tcs.tifr.res.in/event/215
DTSTAMP:20230914T125915Z
SUMMARY:What Risks Lead to Ruin
DESCRIPTION:Speaker: Venkat Anantharam\nUniversity of California\, Berkeley
\nDepartment of Electrical Engineering\nand Computer Science\n\nAbstract:
\nInsurance transfers losses associated with risks to the insurer for a pr
ice\, the premium. We adopt the collective risk approach. Namely\, we abst
ract the problem to include just two agents: the insured and the insurer.
We are interested in scenarios where the underlying model for the loss dis
tribution is not very well known\, and the potential losses can also be qu
ite high\, which is of potential interest\, for instance\, in insuring aga
inst loss-of-use risk for services on offer over the Internet\, where mode
ls for the statistics of the loss are not well established. It is then nat
ural to adopt a nonparametric formulation. Considering a natural probabili
stic framework for the insurance problem\, assuming independent and identi
cally distributed (i.i.d.) losses\, we derive a necessary and sufficient c
ondition on nonparametric loss models such that the insurer remains solven
t despite the losses taken on.\n\nIn more detail\, we model the loss at ea
ch time by a nonnegative integer. An insurerâ€™s scheme is defined by
the premium demanded by the insurer from the insured at each time as a fu
nction of the loss sequence observed up to that time. The insurer is allow
ed to wait for some period before beginning to insure the process\, but on
ce insurance commences\, the insurer is committed to continue insuring the
process. All that the insurer knows is that the loss sequence is a realiz
ation from some i.i.d. process with marginal law in some set $P$ of probab
ility distributions on the nonnegative integers. The insurer does not know
which $p \\\\in{\\\\cal P}$ describes the distribution of the loss sequen
ce. The insurer goes bankrupt when the loss incurred exceeds the built up
buffer of reserves from premiums charged so far.\n\nWe show that a finite
support nonparametric loss model of this type is insurable if it contains
no â€œdeceptiveâ€ distributions. Here the notion of ``deceptiveâ
€ distribution is precisely defined in information-theoretic terms. No
te that\, even though we assume a finite support for each $p \\\\in{\\\\ca
l P}$\, there is no absolute bound assumed on the possible loss at any tim
e. The necessary background from information theory and risk theory as wel
l as some motivation for the problem formulation will be provided during t
he talk (joint work with Narayana Prasad Santhanam (University of Hawaii\,
Manoa)).\n
URL:https://www.tcs.tifr.res.in/web/events/215
DTSTART;VALUE=DATE:20110809
LOCATION:A-212 (STCS Seminar Room)
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