Safety-first portfolio optimization is concerned with maximizing the expected portfolio return subject to a safety-first constraint, which is defined as the probability of failing to achieve a specified target. Commonly the target is assumed to be fixed, which, however, leads to significant...

This paper analyzes the safety-first portfolio model under two different target assumptions, the fixed target, which is commonly assumed in the literature, and the random target, which has played only a minor role so far. As both targets can be easily motivated, the open question is, which...