Function space integration for annuities

David Perry; Wolfgang Stadje

doi:10.1016/S0167-6687(01)00074-9

Function space integration for annuities

David Perry
, Wolfgang Stadje

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	73-82
Number of pages	10
Journal	Insurance: Mathematics and Economics
Volume	29
Issue number	1
DOIs	https://doi.org/10.1016/S0167-6687(01)00074-9
State	Published - 20 Aug 2001

Keywords

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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10.1016/S0167-6687(01)00074-9

Cite this

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AB - 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.

KW - Annuity

KW - Markov time

KW - Random interest rate

KW - Reflected Brownian motion

UR - https://www.scopus.com/pages/publications/0002449984

U2 - 10.1016/S0167-6687(01)00074-9

DO - 10.1016/S0167-6687(01)00074-9

M3 - Article

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JO - Insurance: Mathematics and Economics

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IS - 1

ER -

Function space integration for annuities

Abstract

Keywords

ASJC Scopus subject areas

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