Focus Portfolio Optimization

Fraunhofer ITWM

Portfolio optimization is mainly focused on the determination of an optimal investment strategy on a financial market. More precisely: the investor must decide how many shares of which securities to hold when, in order to maximize his/her utility of wealth at the end of the planning period.

In contrast to option pricing, where for decades continuous time models of financial mathematics are applied in practice, the about 40 years old single period model of Markowitz including several variations remains the basis of investment decisions of fund managers.

In the meantime, the development of modern, time-continuous portfolio optimization has advanced so far that many algorithms are available for practical application and implementation, which have also been carried out at the ITWM. One project in this framework was the development of a online consultation prototype tool that we keep up to date.

We feature:

  • Implementation of typical reference models:
    • The Markowitz One-Period model in many variants (Expectation-Variance, Variance-Expectation, customer-oriented upgrades on general measures of risk)
    • The continuous-time Merton-Model for arbitrary many instruments/assets
  • Extension of the reference models:
    • Optimal investment at Crash threat
    • Consideration of transaction costs
    • Realistic modelling of trading dates (discrete approximation of the Merton Model, the Relaxed Investor Model by Rogers)
    • Optimal assignment of bond portfolios (even with default risk afficted bonds)

Fundamental research:

  • Worst-Case Portfolio-Optimization
  • Realistic transaction models
  • Multi-dimensional Models
  • Portfolio-Optimization with stochastic interest rates
  • Optimal investment at the Principal Agent problem

References and partners