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Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of “Maximum Loss” (ML) is introduced as a method for identifying the worst case in a given scenario space, called “Trust Region”. Next, a technique for calculating efficiently ML for quadratic functions is described; the algorithm is based on the Levenberg-Marquardt theorem, which reduces the high dimensional optimization problem to a one dimensional root finding. |
