The Marginal Price of Risk with a VaR Constraint

The marginal price of risk for a manager who maximizes his firm's expected value given a VaR constraint, otherwise known as a probability-of-ruin or Telser safety-first constraint, is the contract's expected payoff or its expected payoff given that the firm's value equals the floor. This price is applicable to continuous distributions with well-defined unconditional and conditional expectations. It can also be used with power law distributions that have been fitted to commodity and stock returns with finite expectations and infinite variances. In contrast to asset pricing models that price only systematic risk, the marginal price derived here prices total risk and reduces to the Security Market Line formula of the CAPM as a special case