Rare events in finance by PDE methods

Wednesday 7 October 2015 h.11:30, Room 1BC45
Daria Ghilli (Padova, Dip. Mat.)
“Rare events in finance by PDE methods"

Rare events, or tails events, are events which happen only “rarely", in other words, they are situated in the tails of the distribution. Take for example the well-known experiment of tossing a coin: our experience (and also the law of large numbers) says that, after a big enough number of tosses, the most probable value for the empirical mean of the outcomes is 1/2. But what about the probability of being far from 1/2? This is a typical rare event.
The theory who deals with the estimation of tails events is called "large deviations theory" and has many applications, for example, in risk management and finance.
After an introduction to the theory, we consider applications to financial mathematics, concerning the estimation of price of particular type of options (out-of the money) near their maturity. These are typical financial objects whose value deteriorates quickly in time and then are considered, in this context, as rare events.
Our approach - mainly of analytical nature - is different from the classical probabilistic ones.

This seminar will be held as a special event during the OPENING DAY OF THE DOCTORAL SCHOOL.