Sample Path Large Deviations Principles for Poisson Shot Noise Processes and Applications

Large Deviations of Poisson Cluster Processes

“…Furthermore, the LDP for X t,T holds under a weaker condition. To prove this theorem we need Lemma 4.3 below, whose proof can be found in Ganesh, Macci and Torrisi (2005) (see Lemma 2.3 therein).…”

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

“…This follows by the LDP of (εS( · ε )) in D[0, 1] equipped with the topology of uniform convergence (see Ganesh, Macci and Torrisi, 2005, Proposition 3.1), using the same techniques in the proof of Theorem 6.2 of Ganesh, O'Connell and Wischik (2004). …”

“…In particular, we give a Cramér-Lundberg type approximation for ε (u), as ε → 0, and we find a most likely path leading to ruin; moreover we determine an asymptotically efficient law for the simulation of ε (u), as ε → 0. These results are based on sample path large deviations of (X ε (t)) derived by combining the ideas of Freidlin-Wentzell theory (see Freidlin and Wentzell, 1984; see also Dembo and Zeitouni, 1998, section 5.6, page 212) and the sample path large deviations of (S(t)) proved by Ganesh, Macci and Torrisi (2005). As in the work of Asmussen and Nielsen (1995), the results in this paper on the ruin probability, the most likely path leading to ruin and the asymptotic efficient simulation law are presented in terms of local adjustment coefficients.…”

Applications of Mogulskii, and Kurtz-Feng Large Deviation Results to Risk Reserve Processes with Aggregate Claims

“…The LDP for (reserve dependent premium with delayed claims) risk process was studied by Ganesh, Massi and Torrisi (2007) [7,8]. They proved the LDP with respect to the uniform topology in the case of superexponential claims i.e., claims for which the moment generating function is finite for every 0   .…”