Portfolio Selection with p-moment Risk Measure

Specialeforsvar:  Martin Weithaler

Titel: Portfolio Selection with p-moment Risk Measure

Resume: This thesis analyses a terminal wealth problem for an agent who wishes to invest in a Black-Scholes market in order to maximise his expected return while taking risk into account. Inspired by the mean-variance analysis by Markowitz, we seek to find an optimal portfolio selection under a p-moment risk measure. Pedersen & Peskir gave an explicit solution for p=2 in 2013, which we also do, however, we employ static programming by utilising the properties of the complete market to set up a budget constraint rather than work on a Hamilton-Jacobi-Bellman equation. This yields an extra equation when applying the method of Lagrangian multipliers or, in other words, an extra Lagrangian multiplier. This method proves useful for general choices of p>1. In the general case solutions are not explicit but expressed as integrals which are computable by numerical means.

Vejleder: Jesper Lund Pedersen
Censor: Kenneth Bruhn Kristiansen