Repeated optional gambles and risk aversion

We analyze in this paper the effect of age on the optimal dynamic strategy toward repeated independent gambles. When deciding to accept or to reject a lottery that is offered today, the gambler knows how many lotteries can yet be played in the future. We first characterize the optimal dynamic strategy when future lotteries are identically distributed. We show that the existence of future lotteries always increases the willingness to gamble today. When the sequence of lotteries is independent but not identically distributed, we show that this does not need to be true. This analysis can be applied to the problem of investing in indivisible risky investment projects, or to the problem of dynamic optimal insurance demand.