The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of a linear real function plus a scaled mean excess function. We establish a reverse ES optimization formula, which says that a mean excess function at any fixed threshold is...

This paper examines the optimal allocation of risk across generations whose savings mix is subject to illiquidity in the form of uncertain trading costs. We use a stylized two-period OLG framework, where each generation makes a portfolio allocation decision for retirement, and show that...

We examine the role of acquirers’ familiarity with targets’ significant downside risks in M&A. We introduce a measure of a firm’s familiarity with another firm’s business downsides using similarity of their risk factor descriptions. We first show that this measure is distinct from...