Title: Essays on Rational Portfolio Theory

Presenter: Simon Ellersgaard Nielsen, PhD. Student, Math/University of Copenhagen

Time: February 29, 2016, 15:15

Place: HCØ, Auditorium 4, Universitetsparken 5, 2100 Copenhagen Ø


  • Prof. Mogens Steffensen (chairman), MATH, University of Copenhagen

  • Prof. Nicole Branger, University of Muenster

  • Prof. Claus Munk, Copenhagen Business School


This dissertation is a potpourri of articles on the topics of model risk and optimal portfolio selection in stochastic environments. The main concerns are:

  • Demonstrating the effect of erroneous delta hedging in a jump-diffusion economy. What is the nature of the profit-and-loss from a theoretical perspective? From an empirical perspective?

  • Analysing the method by which the non-linear Hamilton-Jacobi-Bellman equations should be solved in connection with Merton type optimisation problems. A thorough review of the explicit and implicit methods is provided in one and more spatial dimensions.

  • Exposing the optimal investment ratios for a utility maximising investor who trades in bonds and stocks in a stochastic volatility environment. Various models are considered, including their effect in empirical trading experiments.

  • Extending the above analysis to include the derivatives markets. How much do the portfolio weights change? What is the effect of hedging stochastic volatility per se versus merely including a second asset? Is the bond-stock-derivative strategy truly superior when applied to real market data?

  • Hedging derivatives in a limit order book with the option of placing both limit and market orders. Assuming a certain tolerance towards deviating from a targeted hedge strategy when should a rational investor place which type of order?

Overall, the project strives to strike a careful balance between theoretical advances and empirical testing of results. An extensive appendix introducing some of the underlying mathematics is provided.


Simon Ellersgaard Nielsen is a PhD student at Math/University of Copenhagen under supervision of Prof. Rolf Poulsen, Math and co-supervisor Assoc. Prof. Ken Friis Larsen, Computer Sciense, University of Copenhagen.

Host: Math and HIPERFIT (Prof. Rolf Poulsen)


29 February 2016