Universite de Lausanne

In the context of surplus models of insurance risk theory, 
some rather surprising and simple identities are presented. This 
includes an
identity relating level crossing probabilities of continuous-time models 
under (randomized) discrete and continuous observations, as well as
reflection identities relating dividend payments and capital injections. 
Applications as well as extensions to more general underlying processes are
discussed.

 

In this talk a number of identities will be discussed that relate to the event of level crossing of certain types of stochastic processes. Some of these identities are surprisingly simple and have interpretations in surplus modelling of insurance portfolios, the design of taxation schemes, optimal dividend strategies and the pricing of barrier options.