This study addresses market concentration among major corporations, highlighting the utility of relative entropy for understanding diversification strategies. It introduces entropic value at risk (EVaR) as a coherent risk measure, which is an upper bound to the conditional value at risk (CVaR),...

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of a Neyman-Pearson type binary solution. We add a constraint on expected return to investigate...

For pension-savers, a low payoff is a financial disaster. Such investors will most likely prefer left-skewed payoff distributions over right-skewed payoff distributions. We explore how such distributions can be delivered. Cautious-relaxed utility measures are cautious in ensuring that payoffs...

This paper proposes a model-free approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions. The generality of this framework allows us to conduct an in-depth theoretical analysis of hedging strategies with a wide family of risk measures...

Pooled annuity products, where the participants share systematic and idiosyncratic mortality risks as well as investment returns and risk, provide an attractive and effective alternative to traditional guaranteed life annuity products. While longevity risk sharing in pooled annuities has...