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Subordinated Brownian Motion: Last Time the Process Reaches its Supremum

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Abstract

The article develops a theory for the last time the subordinated Brownian motion (SBM with negative drift reaches its supremum. The study includes obtaining expressions for the Laplace transform of the last time that the SBM reaches its supremum and also for its density. In the process, we establish that the last time that the SBM reaches its supremum is a member of the generalized gamma convolution (GGC) family. The theoretical results for the general case have been explicitly derived for some well-known subordinators. Numerical investigations show close agreement between the theoretical derivations and empirical computations.

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Authors and Affiliations

  1. Department of Finance & Management Science, Washington State University, Pullman, USA

    Stergios B. Fotopoulos & Yuxing Luo

  2. Department of Mathematics, Washington State University, Pullman, WA, 99164-4746, USA

    Venkata K. Jandhyala

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  1. Stergios B. Fotopoulos
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  2. Venkata K. Jandhyala
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  3. Yuxing Luo
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Correspondence to Stergios B. Fotopoulos.

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Fotopoulos, S.B., Jandhyala, V.K. & Luo, Y. Subordinated Brownian Motion: Last Time the Process Reaches its Supremum. Sankhya A 77, 46–64 (2015). https://doi.org/10.1007/s13171-014-0061-4

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  • DOI: https://doi.org/10.1007/s13171-014-0061-4

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