Let us consider a risk process with reserve-dependent premium rate and delayed claims. Consider a class of risk processes derived from the original one via scaling in a slow Markov walk sense. In this paper we prove sample path large deviations for the class of risk processes. As a consequence, we give exact asymptotics for the logarithm of the ruin probabilities and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient law for the simulation of the ruin probability.
Ganesh, A., Macci, C., Torrisi, G. (2007). A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling. QUEUEING SYSTEMS, 55(2), 83-94 [10.1007/s11134-006-9000-y].
A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling
MACCI, CLAUDIO;
2007-01-01
Abstract
Let us consider a risk process with reserve-dependent premium rate and delayed claims. Consider a class of risk processes derived from the original one via scaling in a slow Markov walk sense. In this paper we prove sample path large deviations for the class of risk processes. As a consequence, we give exact asymptotics for the logarithm of the ruin probabilities and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient law for the simulation of the ruin probability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
