On matrix exponential approximations of the infimum of a spectrally negative Levy process

Florin Avram (1) , Andras Horvath (2) , M.R. Pistorius (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Dipartmento de Informatica
3 Dept. of Mathematics

We recall four open problems concerning constructing high-order matrix-exponential approximations for the infimum of a spectrally negative Levy process (with applications to first-passage/ruin probabilities, the waiting time distribution in the M/G/1 queue, pricing of barrier options, etc). On the way, we provide a new approximation, for the perturbed Cramer-Lundberg model, and recall a remarkable family of (not minimal order) approximations of Johnson and Taaffe , which fit an arbitrarily high number of moments, greatly generalizing the currently used approximations of Renyi, De Vylder and Whitt-Ramsay. Obtaining such approximations which fit the Laplace transform at infinity as well would be quite useful.

Mots clés: Levy process; first passage problem; Pollaczek-Khinchine formula; method of moments; matrix-exponential function; De Prony system; admissible Padé approximation; Johnson-Taaffe approximations; two-point Padé approximations

Domaines: Probabilités [math.PR]

Florin Avram, Andras Horvath, M.R. Pistorius. On matrix exponential approximations of the infimum of a spectrally negative Levy process. 2012. ⟨hal-00739232⟩