Optimal investment with taxes: an optimal control problem with endogeneous delay

The case where portfolio rebalancement involves the payment of taxes on benefits is analyzed. Purchasing time of the asset to be sold is recorded to compute the amount of tax to be paid. The model assumes a no-short-selling constraint and the first-in-first-out priority rule on sales. The agent problem is a nonclassical optimal control problem with endogeneous delay and with complex nonnegativity constraint on consumption. Some additional smoothness conditions on the optimal strategy are assumed to derive the first-order conditions associated with the control problem of interest. The usual variational methods are adapted to handle the endogeneous delay function.