This paper addresses the question of how an institution might optimally manage the market risk of a given exposure. We provide an analytical approach to optimal risk management under the assumption that the institution wishes to minimize its Value-at-Risk (VaR) using options follows a geometric...

Very often, we associate the dawn of modern financial theory with Harry Markowitz who in the 1950s introduced the formal mathematics of probability theory to the problem of managing risk in an asset portfolio. The 1970s saw the advent of formal models for pricing options and other derivative...