The candidate is expected to develop a new area of the portfolio selection theory. Given a reference asset such as a stock index and its individual components, there is a trading strategy that trades in the individual assets subject to no shorting constraints that maximizes the distributional distance to the index. Such a strategy will have the largest volatility with respect to the index. Finding the volatility maximizing strategy requires generalization of the existing comparison theorems to multidimensional case (N>2), which will be a new result. The strategy should be characterized by either an analytical formula in the optimistic scenario, or with a numerical solution if the analytical solution is not available. The thesis should either confirm or reject the hypothesis that the volatility maximizing strategy should fully invest in a single asset at a given time. Furthemore, it is expected that the portfolio with maximal volatility will have some interesting properties, namely it should magnify all potential distributional discrepancies between the real measure and the martingale measure. Trading strategies that use such distributional discrepancies are studied in stochastic portfolio theory, and thus the volatility maximization strategy should be put in the context of this approach.
Seznam odborné literatury
Vecer, J.: Stochastic Finance, A Numeraire Approach, CRC Press, 2011.
Fernholz, R.: Stochastic portfolio theory, Springer, 2002.
Hajek, B.: Mean stochastic comparison of diffusions. Probability Theory and Related Fields, 1985, 68(3), 315-329.
Karatzas, I., Shreve, S.: Brownian motion and stochastic calculus, Springer, 1988.
Předběžná náplň práce
Cílem této disertační práce je najít portfolio s největší možnou volatilitou vzhledem k referenčnímu indexu a studovat vlastnosti takového portfolia.
Předběžná náplň práce v anglickém jazyce
The goal of this doctoral thesis is to find a portfolio with the largest volatility with respect to the reference index and study properties of such a portfolio.
- zadáno a potvrzeno stud. odd.