A note on long-term optimal portfolios under drawdown constraints

The maximization of the long-term growth rate of expected utility is considered under drawdown constraints. In a general situation, the value and the optimal strategy of the problem are related to those of another .standard. risk-sensitive-type portfolio optimization problem. Furthermore, an upside-chance maximization problem of a large deviation probability is stated as a .dual. optimization problem. As an example, a .linear-quadratic. model is studied in detail: the conditions to ensure the solvabilities of the problems are discussed and explicit expressions for the solutions are presented.