IV Simulation

Abstract

Simulation is the technique of examining a problem by playing it through like a game. Usually the problem involves probabilities and these are modelled in the game by a random element introduced by throwing a die, picking numbered counters from a bag or generating random numbers on a computer. Usually the probabilities of interest are estimated by playing through the game a large number of times. It is the speed of the modern computer which has turned the technique from an interesting toy into a powerful tool.As an example suppose we have a problem involving a payment if a life agedxdies before agex+1 and we are givenqx= ·024, say. If we have a bag with counters numbered 1, 2,… 1,000 and pick one at random then the probability that the number drawn is less than or equal to 24 is just ·024. Hence it will be convenient to invent the ‘rule’ that at that point in the game if the number drawn is less than or equal to 24 thenxdies and the payment is made, otherwise he lives and no payment is made.