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A note on multiple life premiums for dependent lifetimes
Affiliation:1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, PR China;2. School of Finance, Southwestern University of Finance and Economics, Chengdu 611130, PR China;3. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5;1. University of Vienna, Faculty of Mathematics, Austria;2. Faculty of Mathematics, University of Montenegro, Montenegro;1. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong;2. Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, PR China;1. School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK;2. Department of Statistics, Actuarial Research Centre, University of Haifa, Mount Carmel, Haifa 3498838, Israel;3. CEPAR, Risk and Actuarial Studies, UNSW Business School, UNSW, Sydney NSW 2052, Australia
Abstract:We study the properties of multiple life annuity and insurance premiums for general symmetric and survival statuses in the case when the joint distribution of future lifetimes has a dependence structure belonging to some nonparametric neighbourhood of independence. The size of the neighbourhood is controlled by a single parameter, which enables us to model really weak as well as stronger dependencies. We provide bounds on the difference of multiple life premiums for vectors of dependent and independent future lifetimes with the same univariate marginal distributions. Each such upper bound can be treated as a premium loading related to the strength of lifetimes’ dependence.
Keywords:Multiple life premium  Dependent future lifetimes  Symmetric status  Survival status  Samaniego’s signatures
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