Elasticity approach to portfolio optimization

We study investment problems in a continuous-time setting and conclude 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, by calculating the optimal elasticities and durations we determine the optimal wealth process and then we compute a portfolio process which tracks these elasticities and durations. Our findings are not only interesting in itself, but the approach also proves useful in many varied applications including portfolios with (path-dependent) options. An important application can be the solution of portfolio problems with defaultable bonds modelled by a firm value approach.