Marcos Escobar-Anel

Abstract We study pre-committed payout design for a retirement tontine whose members share idiosyncratic and systematic longevity risk. Mortality is decomposed into a deterministic interacted-Gompertz age–period baseline and a unit-mean stationary affine residual factor. Population death counts are conditionally Poisson, whereas survivors in the closed cohort are conditionally binomial given the common factor path.

Abstract This paper develops a novel and flexible life-cycle framework, where borrowing human capital plays an explicit role in modeling and decision-making, explicitly impacting risk-aversion levels, borrowing rates, and inter-temporal discount rates. We find the pre-commitment solution to this new ‘double’ optimization problem in semi-closed form in a region of the control/policy space while developing a numerical procedure to approximate the remaining region using the solvable cases.

1. Introduction The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is a discrete-time model widely used in financial analysis and modeling because of its ability to capture the dynamic nature of volatility in economic time series data Bollerslev (1986).