Abstract
0 e-Γ (t-) dΛ (t). In this paper, we develop large deviation theory for D in a context in which the accumulated discount process, Γ, is small. More precisely, in this paper we provide: 1) logarithmic large deviations that hold in great generality in both discrete and continuous time, and 2) exact asymptotics derived in the iid (independent and identically distributed) case and also in the case in which Λ is a Levy process and Γ (t) is a function of a Markov process. This setting is motivated by applications in insurance risk theory with return on investments. Our development of logarithmic asymptotics requires the study of a certain non-standard topology in order to apply contraction principles. Finally, our exact asymptotic results, although analogous to classical results for sums of iid random variables, present important qualitative differences that we also explain here.
Authors
J Blanchet, P Glynn
Publication date
2005/8
Publisher
Working paper
