Essays on Rational Portfolio Theory

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.

Supervisor: Prof. Rolf Poulsen, Math, University of Copenhagen

Co-supervisor: Ass. Prof. Ken Friis Larsen, Computer Sciense, University of Copenhagen

Assessment committee:

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

Prof. Nicole Branger, University of Muenster

Prof. Claus Munk, Copenhagen Business School