### Lump sum or annuity?

#### (Mar 28, 2018)

People are often faced with a decision whether to live off their savings or buy an annuity.  Normally such decisions are made around the retirement ages of 60-65.  However, an interesting counter-example has just been provided by eighteen-year-old Charlie Lagarde, the winner of a lottery in Canada.  She had to decide between taking a C$1million lump sum or an annuity of C$1,000 each week for life.  She opted for the latter, forswearing an opportunity to become an instant millionaire.  But was it the right decision?

We obtained the most recent mortality tables for the population of Quebec and performed some simple calculations of the discounted present value of C\$1,000 per week.  The results are shown in Table…

Tags: annuity, life expectancy

### Some points for integration

#### (Mar 2, 2016)

The survivor function from age $$x$$ to age $$x+t$$, denoted $${}_tp_x$$ by actuaries, is a useful tool in mortality work.  As mentioned in one of our earliest blogs, a basic feature is that the expected time lived is the area under the survival curve, i.e. the integral of $${}_tp_x$$.  This is easy to express in visual terms, but it often requires numerical integration if there is no closed-form expression for the integral of the survival curve.  In this article we look at some of the options available to actuaries who need to integrate numerically.

A general result is that the survivor function has the following form:

${}_tp_x = e^{-H_x(t)}$

where $$H_x(t)$$ is the integrated hazard function:

\[H_x(t) = \int_0^t…

### Insurance or right?

#### (Jan 7, 2013)

The Economist recently carried an article about the perceived unfairness of increasing the retirement age. The argument is that poorer people have higher mortality rates, which means they get less value from a given pension than richer people: the poor are less likely to survive long enough to receive the pension, and if they do they will draw it for a shorter period of time. Of course, a similar argument applies to males or smokers: they have higher mortality rates than females and non-smokers, respectively.

At the root of this problem is the little-discussed question of whether an old-age pension is an insurance or a benefit of right. When the first UK-wide state pension commenced in 1909, a twenty-year-old…

### The limits of limits

#### (May 3, 2011)

Is there a limit to life expectancy?  Oeppen and Vaupel (2002) wrote a very succinct article in which they stated the problem:

"Is life expectancy approaching its limit? Many - including individuals planning their retirement and officials responsible for health and social policy - believe it is. The evidence suggests otherwise."

Oeppen and Vaupel, Broken limits to life expectancy, Science, May 2002

Has anything changed since Oeppen and Vaupel wrote this in 2002?  In terms of mortality rates, the answer is no - mortality rates have continued to fall, especially at post-retirement ages.  Unfortunately, there has only been modest progress in terms of the other problem Oeppen and Vaupel…