Evolutionary behavioural finance (EBF) explores the financial markets as biological systems. Evolutionary process is realized through the interaction between the investment strategies leading to redistribution of the market wealth. Survival is one of the key questions in the analysis of the market selection process. The thesis develops four models using the EBF framework. The models address the following problems: 1) including the riskless asset into the market with short-lived assets; 2) allowing for short selling in the market with short-lived assets; 3) allowing for short selling in the market with long-lived, dividend-paying assets and 4) studying a market with short-lived assets from a game-theoretic perspective with the focus on the analysis of Nash equilibrium properties of survival portfolio rules. In all four cases existence of survival strategies is proved and explicit formulas for such strategies are provided. For the models with short-lived assets it is also shown that the survival strategy is asymptotically unique in a certain class of strategies.