Minimizing coherent risk measures of shortfall in discrete‐time models with cone constraints

Minimizing Shortfall

Shortfall Minimizing Portfolios

Many institutional and private investors seek for a long run excess return relative to a reference strategy (e.g. money market, bond index, etc.) which they want to attain under a minimal shortfall probability. In this article it is shown that even in the long run in order to attain a substantial excess return a high shortfall probability has to be accepted. In the model the prices of the asset...

Shortfall-dependant Risk Measures (and Previsions)

Because of their simplicity, risk measures are often employed in financial risk evaluations and related decisions. In fact, the risk measure ρ(X) of a random variable X is a real number customarily determining the amount of money needed to face the potential losses X might cause. At a sort of second-order level, the adequacy of ρ(X) may be investigated considering the part of the losses it does...

Excess invariance and shortfall risk measures

This paper introduces an axiom of excess invariance for risk measures, meaning insensitivity to the amount by which a portfolio’s value exceeds a benchmark. The paper also introduces the class of shortfall risk measures, which are excess-invariant as well as normalized, non-negative, and monotone non-increasing. Shortfall risk measures are suitable for regulatory or risk management applications...

The Risk and Rewards of Minimizing Shortfall Probability

SUMMER 1999 M any different investment objectives and criteria have been suggested for choosing investment strategies. In a static setting, Markowitz [1952] suggests the meanvariance approach. Economic theory more formally postulates that an individual investor would choose an investment strategy to maximize expected utility of wealth and or consumption. In other settings, other criteria might ...