Jump-Diffusion Models in Finance and Insurance
Centre of Excellence for Mathematics and Statistics of Complex Systems Seminar
by Professor Nikolai Leonenko
Abstract: 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.
[Joint work with F.Avram (Pau, France) and L.Rabehasaina (Besancon, France).]
F.Avram, N.Leonenko and L.Rabehasiana, Series expansions for the first passage distribution of Wong-Pearson jump-diffusion, Stochastic Analysis and Applications, 2009, 27, 770-796
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