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Peer-to-Peer Lending: a Growth-Collapse Model and its Steady-State Analysis

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  • Onno Boxma

    (Eindhoven University of Technology)

  • David Perry

    (Holon Institute of Technology)

  • Wolfgang Stadje

    (University of Osnabrück)

Abstract

We present a stochastic growth-collapse model for the capital process of a peer-to-peer lending platform. New lenders arrive according to a compound Poisson-type process with a state-dependent intensity function; the growth of the lending capital is from time to time interrupted by partial collapses whose arrival intensities and sizes are also state-dependent. In our model the capital level administered via the platform is the crucial quantity for the generated profit, because the brokerage fee is a fixed (small) fraction of it. Therefore we study its steady-state probability distribution as a key performance measure. In the case of exponentially distributed upward jumps we derive an explicit expression for its probability density, for quite general arrival rates of upward and downward jumps and for certain collapse mechanisms. In the case of generally distributed upward jumps, we derive an explicit expression for the Laplace transform of the steady-state cash level density in various special cases. An alternative model featuring up and down periods and a shot noise mechanism for the downward evolution is also analyzed in steady state.

Suggested Citation

  • Onno Boxma & David Perry & Wolfgang Stadje, 2022. "Peer-to-Peer Lending: a Growth-Collapse Model and its Steady-State Analysis," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 233-258, October.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:2:d:10.1007_s00186-022-00793-x
    DOI: 10.1007/s00186-022-00793-x
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    References listed on IDEAS

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    1. Percy H. Brill, 2008. "Level Crossing Methods in Stochastic Models," International Series in Operations Research and Management Science, Springer, number 978-0-387-09421-2, June.
    2. Ivo Adan & Onno Boxma & Jacques Resing, 2022. "Functional equations with multiple recursive terms," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 7-23, October.
    3. Ivo Adan & Brett Hathaway & Vidyadhar G. Kulkarni, 2019. "On first-come, first-served queues with two classes of impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 113-142, February.
    4. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
    5. Bachmann, Alexander & Funk, Burkhardt, 2011. "Online Peer-to-Peer Lending – A Literature Review," Journal of Internet Banking and Commerce, , vol. 16(2), pages 01-18, August.
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    Cited by:

    1. W. Stadje & D. Perry, 2022. "Growth-collapse effects applied to cash management and queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 257-259, April.

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    Keywords

    P2P lending; Compound Poisson; Growth-collapse; Shot noise;
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