Constant Proportion Portfolio Insurance Under Regime Switching Exponential L evy Process

The constant proportion portfolio insurance is analyzed by assuming that the risky asset price follows a regime switching exponential Levy process. Analytical forms of the shortfall probability, expected shortfall and expected gain are derived. The characteristic function of the gap risk is also obtained for further exploration on its distribution. The specific implementation is discussed under some popular L ́evy models including the Merton's jump- diffusion, Kou's jump-diffusion, variance gamma and normal inverse Gaus- sian models. Finally, a numerical example is presented to demonstrate the implication of the established results