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Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables
Author(s) -
Darkiewicz Grzegorz,
Deelstra Griselda,
Dhaene Jan,
Hoedemakers Tom,
Vanmaele Michèle
Publication year - 2009
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/j.1539-6975.2009.01322.x
Subject(s) - annuity , mathematics , life annuity , random variable , brownian motion , upper and lower bounds , regular polygon , econometrics , stochastic process , subadditivity , economics , mathematical economics , statistics , combinatorics , finance , pension , mathematical analysis , geometry
We investigate lower and upper bounds for right tails (stop‐loss premiums) of deterministic and stochastic sums of nonindependent random variables. The bounds are derived using the concepts of comonotonicity, convex order, and conditioning. The performance of the presented approximations is investigated numerically for individual life annuity contracts as well as for life annuity portfolios, where mortality is modeled by Makeham's law, whereas investment returns are modeled by a Brownian motion process.