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Continuous-time perpetuities and time reversal of diffusions

Author

Listed:
  • Constantinos Kardaras

    (London School of Economics)

  • Scott Robertson

    (Carnegie Mellon University)

Abstract

We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markovian model. Two approaches are used to obtain the distribution. The first identifies a partial differential equation for the conditional cumulative distribution function of the perpetuity given the initial factor value, which under certain conditions ensures the existence of a density for the perpetuity. The second (and more general) approach, using techniques of time reversal, identifies the joint law as the stationary distribution of an ergodic multidimensional diffusion. This latter approach allows efficient use of Monte Carlo simulation, as the distribution is obtained by sampling a single path of the reversed process.

Suggested Citation

  • Constantinos Kardaras & Scott Robertson, 2017. "Continuous-time perpetuities and time reversal of diffusions," Finance and Stochastics, Springer, vol. 21(1), pages 65-110, January.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:1:d:10.1007_s00780-016-0308-0
    DOI: 10.1007/s00780-016-0308-0
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    References listed on IDEAS

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    More about this item

    Keywords

    Perpetuities; Time reversal; Ergodic diffusions; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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