Rare events

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Rare events arise, often with catastrophic consequences, in fields such as finance, manufacturing and telecommunications. A rare event might be large number of claims in a short period of time bankrupting an insurance company or an unexpectedly high rate of packet arrivals may cause a buffer overload in a telecommunications system. Rare events are difficult to simulate precisely because the event of interest occurs so rarely. The proposal is to calculate the probability of particular large deviations, and find the most probable path. These two pieces of information can help redesign a system to make the rare event even less likely. Of particular interest are large deviations where the most probable path is nonlinear; i.e. it is sometimes the case that one gets sideswiped by a rare event in another part of the system whose failure cascades across the network. A recent idea of an approximate time reversal seems to be the key to solving these nonlinear problems. The applicant hopes to apply these methods to finance (R. Nikzad is working on a problem relevant to the bank of Canada) to rare event simulation (Jesse Collingwood is doing his Ph.D. on rare events in engineering) and to telecommunications.