Speaker: Lane P. Hughston, Imperial College London

Title: Zeta processes and their financial applications

Abstract: The zeta distribution, sometimes also called the Zipf
distribution, is the discrete analogue of the so-called Pareto
distribution, and has been used to model a great variety of
interesting phenomena with fat-tailed behaviour. It makes sense 
therefore to consider financial contracts for which the payoff 
is represented by a random variable of that type. This talk 
will present an overview of some of the basic properties of the 
zeta distribution and the associated multiplicative Levy 
process, which we shall call the zeta process, with a view to 
financial applications, both in risk management and in the 
design of new contracts. A simple model for a security with a 
Zipfian payoff is constructed satisfying the conditions 
required to ensure absence of arbitrage. Based on work with D. 
Brody, S. Lyons, and M. Pistorius.