The Elasticity Approach to Portfolio Optimization

We consider investment problems in a continuous-time setting and show that the proper control variables are elasticities to the traded assets or, in the case of stochastic interest rates, (factor) durations. This formulation of a portfolio problem allows us to solve the problems in a kind of two-step procedure: First, calculating the optimal elasticities and durations which determine the optimal wealth process and then computing a portfolio process which tracks these elasticities and durations. Our findings are not only important by itself but the approach also turns out to be useful in many applications, for example for portfolios with (path-dependent) options