Asset allocation is one of the central issues in banking, finance and insurance industries. Using ruin probability and expected loss at ruin as measures of risk, we aimed to inves­tigate the optimal investment problem of an investor in finance and insurance in a static one-period setting. Mean - Variance, Value at Risk (VaR) and Conditional Value at Risk (CVaR) model­ing were three approaches investigated in this thesis. However, mathematically VaR had some serious limitations, such as lack of sub-additivity. In the case of a finite number of scenarios, VaR is a non-smooth, non-convex function, making it difficult to control and optimize. This fact stimulate our development of new optimization algorithms presented here, by introducing ruin probability and expected loss at ruin. Optimization problems with a certain level of expected return in finance field were first analyzed and then with premium and claim loss added into consideration, the optimization methodologies were applied to the insurance field. After introducing ruin probability and expected loss at ruin as risk measures, the optimization results became more accurate and feasible. Using our proposed new method, we investigated the capital required and asset allo­cation problem.