Søren Asmussen (Aarhus University): On Wiener-Hopf Factorization and Erlangization in Regime-Switching Financial Lévy Models (Joint Seminar with OR)

Please join us for a joint seminar of the Advanced Financial Technologies Laboratory (AFTLab) and the Operations Research (OR):

Time: Thursday, April 30, 2026, 5:00pm-6:00pm

Location: Huang 305 

Speaker: Søren Asmussen (Aarhus University) 

Title: On Wiener-Hopf Factorization and Erlangization in Regime-Switching Financial Lévy Models

Abstract: The Wiener-Hopf factorization of a Lévy process X at an independent exponential time e₁ states that the maximum X̄(e₁) and the displacement X̄(e₁)−X(e₁) from the terminal value are independent. We present an extension to regime-switching models up to a more general time horizon. This covers in particular Canadization/Erlangization, meaning that a fixed maturity T is approximated by an Erlang r.v. e_q(T) (a sum of q i.i.d. exponentials) with mean T. Under the traditional assumption in barrier and lookback option pricing that jumps are hyperexponential, we present an iterative matrix algorithm for the marginal distributions of the Wiener-Hopf factors. From this together with the factorisation, prices, Greeks etc. come out as limits as q→∞ of closed matrix expressions. Here Richardson extrapolation allows to keep q and hence matrix dimensions quite small. The approach avoids otherwise dominant features in the literature such as numerical transform inversion and expansions in terms of roots determined by analytic continuation and Rouché's theorem. The class of models is dense in the whole space of càdlàg processes. A number of examples are presented, including stochastic or time-varying volatilities.

More information on the Advanced Financial Technologies Laboratory (AFTLab): https://fintech.stanford.edu/ and upcoming seminars: https://fintech.stanford.edu/events/series/aftlab-seminars