PhD Defence: Simon Ellersgaard Nielsen
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)