Abstract
We introduce a novel way of modeling the dependence of coupled lifetimes, for the pricing of joint and survivor annuities. Using a well-known Canadian data set, our results are analyzed and compared with the existing literature, mainly relying on copulas. Based on urn processes and a one-factor construction, the proposed model is able to improve its performances over time, in line with the machine learning paradigm, and it also allows for the use of experts' judgements, to complement the empirical data.
Highlights
We propose a novel nonparametric approach to the modeling of joint and survivor annuities, useful in the case of right-censored observations
Knowing the original distribution will allow us to estimate the difference between the original distribution and the posterior computed through Markov Chain Monte Carlo (MCMC), and to study how these differences affect the final price of the annuity
The rest of the section is structured as follows: in Subsection 5.2.1 we show the Bivariate Reinforced Urn Process (B-Reinforced Urn Process (RUP)) estimation of the joint survival function, and in Subsection 5.2.2 the relative annuity calculations; in Subsection 5.2.3, we compare our results with the copula approach one can find for example in Frees et al (1996)
Summary
We propose a novel nonparametric approach to the modeling of joint and survivor annuities, useful in the case of right-censored observations. To a particular class of models (Muliere et al, 2000; Walker and Muliere, 1997) with the extremely useful ability of combining some a priori knowledge–possibly referring to experts’ judgements–with the information coming from actual data, perfectly in line with the Bayesian paradigm This possibility allows for the incorporation of trends, tail events or other aspects that can be rarely observed in a data set– invisible to standard machine learning approaches, yet possible and with dramatic consequences (Taleb, 2007). Nothing guarantees the ability of eliciting a sound and reliable a priori: experts could naturally be wrong The answer to such a relevant observation–we shall see–is that the bivariate urn model learns over time, at every interaction with actual data.
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