We study whether prices of traded options contain information about future extreme market events. Our option-implied conditional expectation of market loss due to tail events, or tail loss measure, predicts future market returns, magnitude, and probability of the market crashes, beyond and above...

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...

We consider a one-period portfolio optimization problem under model uncertainty. For this purpose, we introduce a measure of model risk. We derive analytical results for this measure of model risk in the mean-variance problem assuming we have observations drawn from a normal variance mixture...