We study the firmly of risk asset in the constant proportion portfolio insurance (CPPI) trading strategy in Hawkesjump-diffusion model where the price of the underlying asset may experience negative jumps. We solve the dynamic of risk asset and cushion by using a mean version stochastic differential Equation under Geometric Brownian Motion. The main goal of portfolio insurance is to protect investors against adverse market movement. We consider the problem of optimal portfolio construction through the dynamics programming and its associate HJB equation of a two-dimensional to solve the supreme of portfolio weights by considering an investors of log, power and exponential utility function. The optimal portfolio model react to each change in jump intensity accordingly. It was observed that, the higher the value of volatility and jump size, the less the expected terminal portfolio. Therefore, the best payoff can be achieved with the increase in number of re-balancing the optimal portfolio weights. And hence reduce the risk of breaching the designed floor.

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