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A factorization of a Lévy process over a phase-type horizon

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This note provides a factorization of a Lévy pocess over a phase-type horizon τ given the phase at the supremum, thereby extending the Wiener–Hopf factorization for τ exponential. One of the factors is defined using time reversal of the phase process. It is shown that there are a variety of time-reversed representations, all yielding the same factor. Consequences of this are discussed and examples provided. Additionally, some explicit formulas for the joint law of the supremum and the terminal value of the process at τ are given.

Original languageEnglish
JournalStochastic Models
Pages (from-to)397-408
Number of pages12
Publication statusPublished - 2018

    Research areas

  • phase-type distribution, splitting, time reversal, Wiener–Hopf factorization, WIENER-HOPF FACTORIZATION, LAW, MARKOV-ADDITIVE PROCESSES, 1ST PASSAGE, Wiener-Hopf factorization, POSITIVE JUMPS

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