Series Expansions for the First Passage Distribution of Wong-Pearson Jump-Diffusions

Florin Avram (1) , Nikolai Leonenko (2) , Landy Rabehasaina (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 School of Mathematics [Cardiff]
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We explore the Erlang series approach for the first-time passage problem for a particular class of jump-diffusions with polynomial state-dependent coefficients. This approach may be viewed as a discrete analog of the Laplace transform, which replaces the differential equations with polynomial coefficients satisfied by this function by algebraic recurrences. We identify cases in which the expansion is finite and in which the recurrence is of second order, and thus more easily solved.

Mots clés: Erlang series; First time passage problem; Jump-diffusion models; Wong-Pearson diffusions

Domaines: Probabilités [math.PR]

Florin Avram, Nikolai Leonenko, Landy Rabehasaina. Series Expansions for the First Passage Distribution of Wong-Pearson Jump-Diffusions. Stochastic Analysis and Applications, 2009, 27 (4), p. 770 - 796. ⟨10.1080/07362990902976611⟩. ⟨hal-00488316⟩