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Continuous-time perpetuities and time reversal of diffusions

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  • Kardaras, Constantinos
  • Robertson, Scott

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

  • Kardaras, Constantinos & Robertson, Scott, 2017. "Continuous-time perpetuities and time reversal of diffusions," LSE Research Online Documents on Economics 67495, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:67495
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    References listed on IDEAS

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    Cited by:

    1. Yakovlev, Andrey A. (Яковлев, Андрей А.) & Freinkman, Lev M. (Фрейнкман, Лев М.) & Makarov, Sergey A. (Макаров, Сергей А.) & Pogodaev, Victor S. (Погодаев, Виктор С.), 2018. "The Elite Consensus and Regional Economic Development: The Experience of the Republic of Tatarstan [Элитный Консенсус И Экономическое Развитие Региона: Опыт Республики Татарстан]," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 180-217, February.

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    More about this item

    Keywords

    PerpetuitiesTime reversalErgodic diffusionsMonte Carlo simulation;

    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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