Optimal Portfolios Under Dynamic Shortfall Constraints

Value-at-Risk (VaR), a downside risk measure, has emerged as the industry standard with regulatory authorities enforcing its use in risk measurement and management. Despite its widespread acceptance, VaR is not coherent. Tail Conditional Expectation (TCE), on the other hand, for an underlying continuous distribution, is a coherent risk measures. Our focus in this paper is the dynamic portfolio and consumption choice of a trader subject to a risk limit specified in terms of TCE.