### Pricing Catastrophe Put Options Using Methods in Ruin Theory

- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Tuesday, November 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Sheldon Lin – Department of Statistics, University of Toronto

The discounted penalty function proposed in the seminal paper
Gerber and Shiu (1998) has been widely used to
analyze the time of ruin,
the surplus immediately before ruin and the deficit at ruin
of insurance risk models in ruin theory.
However, few of its applications can be found beyond,
except that Gerber and Landry (1998)
explored its use for the pricing of perpetual American put options. In
this talk,
I will discuss the use of the discounted penalty function and mathematical
tools
developed for the function
for perpetual American catastrophe
put options. Assuming that catastrophe losses
follow a mixture of Erlang distributions,
I will show that an analytical (semi-closed) expression for the price of
perpetual American catastrophe put options can be obtained.
I will then discuss
the fitting of a mixture of Erlang distributions to catastrophe loss
data using an EM algorithm.