Value-preserving portfolio strategies in the minimal market model

Abstract A value-preserving portfolio strategy is based on the idea that every generation should hand over a portfolio of the same value to the next generation as it received from the foregoing one. Hence, only economic gains can be consumed. Given a natural definition of the portfolio value, the underlying theoretical concept has various features in common with the benchmark approach of Eckhard Platen. In this contribution, we develop a generalization of value preserving portfolio strategies that allows their construction in the framework of the so-called minimal market model of the benchmark approach. This framework is particularly suited for the value-preserving concept as we consider a long-term investment horizon for which the popular constant market coefficient settings based on geometric Brownian motions or jump diffusions are not flexible enough. Further, we demonstrate the application of the value-preserving concept using real market data. In particular, the use of the minimal market model framework allows one to overcome estimation problems for stock returns.