Buy-and-Hold Strategies and Comonotonic Approximations

We investigate optimal buy-and-hold strategies for terminal wealth problems in a multi-period framework. As terminal wealth is a sum of dependent random variables, each of these variables corresponding to an amount of capital that has been invested in a particular asset at a particular date, we first consider approximations that reduce the multivariate randomness to univariate randomness. Next, these approximations are used to determine buy-and-hold strategies that optimize, for a given probability level, the Value at Risk and the Conditional Left Tail Expectation of the distribution function of final wealth. This paper complements Dhaene et al. (2005), where the case of continuous rebalancing is considered.