We study portfolio selection in a one-period financial market with an Expected Shortfall (ES) constraint. Unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage and show that the presence or absence of...

This paper studies mean-risk portfolio selection in a one-period financial market, where risk is quantified by a star-shaped risk measure ρ. We introduce two new axioms: weak and strong sensitivity to large losses. We show that the first axiom is key to ensure the existence of optimal...

In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black-Scholes-Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down a candidate value function and to use a verification...

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique...