This thesis deals with different models for decision-making under risk in financial applications, mainly models that incorporate irrational human behavior. First of all, traditional expected utility theory is considered. Hereafter, two models that incorporate irrational human behavior are discussed and compared: prospect theory and cumulative prospect theory. Next, these models are applied to option pricing. The influence of various levels of sentiment on the option price is investigated and the prices are compared with Black-Scholes prices. Also, a sensitivity analysis is done in order to investigate the influence of the prospect parameters on the option price. Furthermore, the different models discussed are applied to portfolio management for which the optimal wealth profiles are analyzed and compared. Moreover, a data analysis with a portfolio of stocks of different indices is done in which it is investigated whether the parameter estimates used for prospect sentiment are applicable to financial data. Finally, a hedge test under prospect sentiment is performed in order to investigate whether a delta-hedge leads to sufficient results in case of asset price paths under prospect sentiment.