Abstracts
Résumé
Les garanties de rachat viager (GLWB) ont fait l’objet de nombreuses analyses dans la littérature en raison de leur risque financier, mais peu d’articles ont jusqu’ici traité de l’option offerte au contractant par rapport au choix du moment de décaissement et ses impacts sur la rentabilité du produit auprès de l’assureur.
Cet article étend l’analyse effectuée par [Huang et al., 2014] dans leur article portant sur le choix optimal de décaissement pour un produit avec garanties de rachat viager. Tout d’abord, nous ajoutons une dimension additionnelle dans l’analyse pour tenir compte de la distribution des pertes d’un assureur selon l’âge au décaissement choisi par le contractant. Ensuite, nous développons un cadre d’analyse novateur afin de déterminer numériquement dans quelle mesure un assureur devrait modifier son échelle de frais lorsque ce dernier s’attend à ce qu’un assuré choisisse un moment de décaissement lui permettant de maximiser sa valeur de contrat. Nous démontrons que le niveau de frais équitables est fonction de l’âge à l’émission de l’assuré. Cette observation va à l’encontre de la pratique et de la structure présente de frais au sein de l’industrie canadienne où les assureurs chargent un niveau de frais uniformes indépendamment de l’âge à l’émission de l’assuré.
Abstract
The extant literature on the Guaranteed Lifetime Withdrawal Benefits (GLWB) financial risk is abundant, however, few articles investigate the option offered to the policyholder with respect to the initiation of the contract and examine this impact on the profitability of the product for the insurer.
We extend the analysis carried out by Huang et al. (IME, 2014) on the optimal initiation of the product with GLWB. First, we add an additional dimension in the analysis to account for the insurer losses as a function of the age for disbursement chosen by the policyholder. Then, we develop a novel analytical framework to determine by numerical methods the extent to which an insurer, expecting his client to choose when to receive benefits to maximize the value of his variable annuity contract, should change its actuarially fair fee structure. We show that the fair premium is a function of the insured policyholder age when he bought the contract. This result runs counter to the current fee structure and practice in the Canadian insurance industry with insurers charging a uniform level of fees regardless of the policyholder biological age when the contract is issued.
Appendices
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