Optimal Portfolios Under Dynamic Shortfall Constraints

Abstract

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.

Keywords and phrases : Value-at-Risk, Tail Conditional Expectation, dynamic portfolio and consumption choice, risk measurement and management.