Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits
Tóm tắt
This paper studies the distribution of particular weighted sums of Bernoulli random variables. The computing methods are applied to derive the probability distribution of the random amount of survivor credits to be shared among surviving participants in single-period tontine schemes. The effectiveness of this new arrangement can then be evaluated beyond the classical analysis based on crude approximations for the two first moments, only.
Tài liệu tham khảo
Chen A, Hieber P, Klein J (2017) Tonuity: a novel individual-oriented retirement plan. Available at https://ssrn.com/abstract=304301
De Pril N (1989) The aggregate claims distribution in the individual model with arbitrary positive claims. ASTIN Bulletin 19:9–24
Dhaene J, Vandebroek M (1995) Recursions for the individual model. Insurance: Mathematics and Economics 16:31–38
Dhaene J, Ribas C, Vernic R (2006) Recursions for the individual risk model. Acta Math Appl Sin Engl Ser 14:632–652
Donnelly C (2015) Actuarial fairness and solidarity in pooled annuity funds. ASTIN Bulletin 45:49–74
Donnelly C, Young J (2017) Product options for enhanced retirement income. Br Actuar J 22:636–656
Donnelly C, Guillen M, Nielsen JP (2014) Bringing cost transparency to the life annuity market. Insurance: Mathematics and Economics 56:14–27
Forman JB, Sabin MJ (2017) Survivor funds. Pace Law Review 37:204–291
Milevsky MA, Salisbury TS (2016) Equitable retirement income tontines: mixing cohorts without discriminating. ASTIN Bulletin 46:571–604
Panjer HH, Wang S (1993) On the stability of recursive formulas. ASTIN Bulletin 23:227–258
Sabin MJ (2010) Fair tontine annuity. Available at https://ssrn.com/abstract=1579932
Sabin MJ, Forman JB (2016) The analytics of a single-period tontine. Available at https://ssrn.com/abstract=2874160
Stamos MZ (2008) Optimal consumption and portfolio choice for pooled annuity funds. Insurance: Mathematics and Economics 43:56–68
Sundt B, Vernic R (2009) Recursions for convolutions and compound distributions with insurance applications. Springer, Berlin
Waldmann KH (1994) On the exact calculation of the aggregate claims distribution in the individual life model. ASTIN Bulletin 24:89–96