Optimal Investment with Taxes : An Existence Result

We study the deterministic control problem of maximizing utility from consumption of an agent who seeks to optimally allocate his wealth between consumption and investment in a financial asset subject to taxes on benefits with first-in-first-out priority rule on sales. Short-sales are prohibited and consumption is restricted to be nonnegative. Such a problem has been introduced in a previous paper by the same authors where the first order conditions have been derived. In this paper, we establish an existence result for this non-classical optimal control problem