The Competitive Investor Game from Bell & Cover (1980) and the 푘-Player Ranking Game from Alpern & Howard (2017) are analysed in thesis. Optimal strategies have been derived and the related proofs have been given a new look. The Symmetric Multiplayer Ranking Game is considered as the general interpretation of financial competition among hedge funds. This study focused on the hedge funds that manage a Long/Short U.S. Equity strategy. Some minor evidence has been found to support the hypothesis that the studied hedge funds manage a strategy that has the objective to beat the competition in terms of annual performance in order to achieve the highest ranking.

Model selection starts with a dataset and a number of candidate models that can explain that data. The AIC and BIC criteria prevents choosing the best fitting model by penalizing for the number of parameters in a model and instead selects the model that performs best when assessed to unseen data. Their performance depends on the sample size and the noise in the data. In portfolio management, it is common to find a combination of financial products such that an objective is optimized. A common risk measure criterion that gets maximized is the Sharpe ratio. Since portfolio management is also done based on historic data, but wanted to be optimized for unseen data, model selection can be applied to portfolio management as well. Finding the optimal weights in a portfolio is done by solving a linear system of equations. Applying this to subsets of stocks which are contained in the AEX index, leads to higher in-sample Sharpe ratios than using equal weights or just following the AEX index. The out-of-sample Sharpe ratio gets overestimated by noise fit and estimation error. The Sharpe Ratio Information Criterion (SRIC) corrects for this. This criterion gives an unbiased estimate for the out-of-sample Sharpe ratio and can be used for model selection in portfolio management. Using a trend following strategy, investing proportionally to the returns, also increases your expected out-of-sample Sharpe ratio.