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Abstract
In this paper, we analyse and construct a lifetime utility maximisation model with hyperbolic discounting. Within the model, a number of assumptions are made: complete markets, actuarially fair life insurance/annuity is available, and investors have time-dependent preferences. Time dependent preferences are in contrast to the usual case of constant preferences (exponential discounting). We find: (1) investors (realistically) demand more life insurance after retirement (in contrast to the standard model, which showed strong demand for life annuities), and annuities are rarely purchased; (2) optimal consumption paths exhibit a humped shape (which is usually only found in incomplete markets under the assumptions of the standard model).
Highlights
With the declining mortality rates, life expectancy has been improved over the last few decades and is one key driver of the ageing population all over the world (World Health Organization 2015).Retirees with longer life expectancy are increasingly exposed to longevity risk.Improved life expectancy can generate more financial burden for governments that provide social security
Low demand for voluntary annuitisation is observed among people, and is known as the annuity puzzle
To measure the impacts of the impatience degree on agent behaviour, we present a number of graphical illustrations of the expected consumption path and the expected insurance premium trajectories for different ζ values in Figures 1 and 2 and compare them to the behaviour of agents with exponential preferences
Summary
With the declining mortality rates, life expectancy has been improved over the last few decades and is one key driver of the ageing population all over the world (World Health Organization 2015). From Purcal and Piggott (2008), this “discount” function generates a bequest that provides a continuous annuity certain that commences at the time of the decease of the investor and ends at the limiting age, ω, of the life table, having assumed that the investor and spouse are the same age. This continuous annuity is assumed to pay 2/3 of the consumption level at the time when the investor dies, m(t) =. It can be any function that impacts the bequest motive directly
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