Quasi-Monte Carlo Methods in Finance with Application to Optimal Asset Allocation

Portfolio optimization is a widely studied problem in finance. The common question is, how a small investor should invest his wealth in the market to attain certain goals, like a desired payoff or some insurance against unwished events.

The starting point for the mathematical treatment of this is the work of Harry Markowitz in the 1950s. His idea was to set up a relation between the mean return of a portfolio and its variance. In his terminology, an efficient portfolio has minimal variance of return among others with the same mean rate of return. Furthermore, if linear combinations of efficient portfolios and a riskless asset are allowed, this leads to the market portfolio, so that a linear combination of the risk-free asset and the market portfolio dominates any other portfolio in the mean-variance sense. ...