Simulation and survival

(Dec 6, 2009)

In an earlier post we discussed how a survival model was directly equivalent to assuming future lifetime was a random variable.  One consequence of this is that survival models make it quick and simple to simulate a policyholder's future lifetime for the purposes of ICAs and Solvency II.

The survival curve is the proportion of lives surviving to each age, i.e. tpx in actuarial parlance.  Below is a sample survival curve in red for a life aged x, showing how to read off the probability of survival to age x+t:

Simulating future lifetime from the survival curve

For simulation purposes we simply reverse this procedure: we generate a pseudo-random number uniformly distributed over the interval (0, 1), place it on the vertical axis and look up the age at death x+t.

A huge…

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Tags: survival curve, ICA, Solvency II, integrated hazard function

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