J. Villarroel Rodriguez
Renewal processes are generalizations of the classical (compound) Poisson process where the waiting times are iidrv with general distribution. Let $X_t$ be such a process. We consider the issue of how those statistics contingent on the actual state-like exit times- are affected depending on whether the actual time is or not a jump time. We suppose that the only available information is the present state $X_r=x$. The answer involves ideas drawn from classical renewal theory. Implications to risk theory are clear: by allowing the classical Lundberg-Cramer model to have arbitrary i.i.d. holding times those results derived at jump times will not carry over to arbitrary present due to the lack of Markoviannes. In particular exit times depend on the actual stateand available information. Here we consider mean ruin times assuming that the present is not necessarily a jump instant, and also a partial knowledge from the observer.
Palabras clave: renewal processes, waiting times, mean exit times
Programado
VD7 Modelos estocásticos
20 de abril de 2012 15:30
Sala Roma II
