Speaker: |
Venkat Anantharam University of California, Berkeley Department of Electrical Engineering and Computer Science |

Date: |
Tuesday, 9 Aug 2011 (all day) |

Venue: |
A-212 (STCS Seminar Room) |

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In more detail, we model the loss at each 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 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 $P$ of probability distributions on the nonnegative integers. The insurer does not know which $p \\in{\\cal P}$ describes the 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 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. Note that, even though we assume a finite support for each $p \\in{\\cal P}$, there is no absolute bound assumed on the possible loss at any time. The necessary background from information theory and risk theory as well as some motivation for the problem formulation will be provided during the talk (joint work with Narayana Prasad Santhanam (University of Hawaii, Manoa)).