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.L. (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

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - Probabilita' e Statistica Matematica
English
Importance sampling; Large deviations; Poisson shot noise; Risk processes; Ruin probabilities
Ganesh, A., Macci, C., & Torrisi, G.L. (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].
Ganesh, A; Macci, C; Torrisi, G
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/34780
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 10
social impact