Function space integration for annuities

David Perry, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


We derive explicit formulas for the expected values of annuities with a random interest rate, modeled by a reflected Brownian motion at zero (RBM) stopped by certain Markov times. We consider times τ of the following kinds: (i) τ is constant, (ii) τ is a random and independent of the RBM X, (iii) τ is the first time X reaches a prespecified level, and (iv) minima of these stopping times. The case of Brownian motion without reflection is also briefly discussed.

Original languageEnglish
Pages (from-to)73-82
Number of pages10
JournalInsurance: Mathematics and Economics
Issue number1
StatePublished - 20 Aug 2001


  • Annuity
  • Markov time
  • Random interest rate
  • Reflected Brownian motion

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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