A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

  • Authors:

  • A. Ganesh;C. Macci;G. L. Torrisi

  • Affiliations:

  • Microsoft Research, 7 J J Thomson Avenue, Cambridge, UK;Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, Roma, Italia;Istituto per le Applicazioni del Calcolo "Mauro Picone" (IAC), Consiglio Nazionale delle Ricerche (CNR), Roma, Italia

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2007

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Abstract

Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(X 驴 (t)): 驴 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let 驴_驴(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X 驴 (t)) as 驴 驴 0. As a consequence, we give exact asymptotics for log 驴_驴(u) and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient law for the simulation of 驴_驴(u).