Second-Best Risk Sharing With Incomplete Contracts

We analyze in this paper the effect of age on the optimal dynamic strategy towards repeated independent gambles. When deciding to accept or to reject a lottery that is offered today, the gambler knows how many future lotteries can yet be played in the future. We first examine under which condition on the utility function the option to gamble in the future decreases aversion to current risks. We also characterize the optimal dynamic strategy when future lotteries are identically distributed and absolute risk aversion is decreasing. This analysis can be applied to the problem of investing in indivisible risky investment projects, or to the problem of dynamic optimal insurance demand. \