Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments August 31, 2015 erstellt
Description:
There is growing interest in the design of annuities that insure against idiosyncratic longevity risk while pooling and sharing systematic risk; for example Piggott, Valdez and Detzel (2005) or Donnelly, Guillen and Nielsen (2014). In this paper we generalize the natural retirement income tontine introduced by Milevsky and Salisbury (2015), by combining heterogeneous cohorts into one pool. We engineer this scheme by allocating tontine shares at either a premium or a discount to par based on both the age of the investor and the amount they invest. For example, a 55 year-old allocating $10,000 to the tontine might be told to pay $200 per share and receive 50 shares, while a 75 year-old allocating $8,000 might pay $40 per share and receive 200 shares. They would all be mixed together into the same tontine pool and each tontine share would have equal income rights. On a historical note, this echoes a proposal by Charles Compton (1833) almost two centuries ago, which hasn't received much attention in the literature. The current paper addresses existence and uniqueness issues and discusses the conditions under which Compton's scheme can be constructed equitably – which is distinct from fairly – even though it isn't optimal for any cohort. As such, this also gives us the opportunity to differentiate between arrangements that are socially equitable, vs. actuarially fair vs. economically optimal