Portfolio insurance strategies are designed to enable investors to limit downside risk while at the same time to gain profits from rising market. Among that, constant proportion portfolio insurance strategy (CPPI) and option-based portfolio insurance strategy (OBPI) are two typical strategies in portfolio insurance strategies. With the popularity of the portfolio insurance strategies, portfolio optimization problem receives plenty of publicity. Each investor has their own preference for return and risk, investment activities should follow a utility function of return and risk. Therefore, portfolio optimization problem can be modeled as expected utility maximization problems. It is well-known that in the Black-Scholes model, these strategies can be implemented as the optimal solution by forcing an exogenously given guarantee to maximize the expected utility of investors with constant relative risk aversion (CRRA) function. In this research, we combine CRRA utility maximization with the stylized strategies and bring these results together. In particular, we focus on the volatile market and consider the market is under the Constant Elasticity of Variance (CEV) model. In addition, we discuss the advantages and disadvantages of CPPI and OBPI strategies under the distribution of terminal wealth process and utility value in CEV model
