City Research Online

Surplus analysis for variable annuities with a GMDB option

Haberman, S. & Piscopo, G. (2010). Surplus analysis for variable annuities with a GMDB option (Actuarial Research Paper No. 193). London, UK: Faculty of Actuarial Science & Insurance, City University London.


In this paper, we analyze the insurance surplus for a Variable Annuity contract with a Guaranteed Minimum Death Benefit (GMDB) option. Initially, we derive the first two moments of the distribution of the surplus; and subsequently, we develop the whole distribution using a stochastic model which involves an integrated analysis of financial and mortality risk for a portfolio of annuities with GMDB embedded options. We offer a model according which the premium can be modified as per the forecasts of mortality probabilities, interest rate and fund evolution. Moreover, the study enables us to determine the premium that leads to a required probability of insolvency, and so it can be used for an evaluation of the adequacy of solvency. Numerical examples illustrate the results.

Publication Type: Monograph (Working Paper)
Publisher Keywords: Guaranteed Minimum Death Benefit option, financial risk, mortality risk, surplus, variable annuity
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance > Actuarial Research Reports
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