● The classic Markowitz model that optimizes for the Sharpe ratio has proven to be suboptimal. ○ Summary is used directly as prediction. ○ Variance is not a good risk measurement since it penalizes positive shocks and says little about tail risks ● Other risk measurements such as Value-at-Risk and Expected Shortfall introduce non-linear, non-convex risk constraints and render the mean-variance ...

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functio...

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Academics and practitioners usually optimize portfolios on the basis of mean and variance. They set the goal of maximizing risk-adjusted returns measured by the Sharpe ratio and thus determine their optimal exposures to the assets considered. However, there is an alternative criterion that has an equally plausible underlying idea; geometric mean maximization aims to maximize the growth of the c...

Stating a confidence interval is a traditional method of indicating the sampling error of a point estimator of a model’s performance measure. We propose a single dimensionless criterion, inspired by Schruben’s coverage function, for evaluating and comparing the statistical quality of confidenceinterval procedures. Procedure quality is usually thought to be multidimensional, composed of the mean...

In this short note we prove a conjecture posed in Cui et al. (2012): Dynamic mean-variance problems in arbitrage-free, complete financial markets do not allow free cash flows. Moreover, we show by investigating a benchmark problem that this effect is due to the performance criterion and not due to the time inconsistency of the strategy.