Portfolio insurance strategies in a jump diffusion setting
Portfolio insurance (PI) strategies enable investors to mitigate downside risk while still retaining the potential for upside gains. This is achieved by maintaining an exposure to risky assets proportional to the difference between the portfolio value and the present value of the guaranteed amount. While PI strategies are known to be free of downside risk in diffusion modeling frameworks with continuous trading real market applications exhibit a significant non-negligible risk, known as gap risk, which increases with the multiplier value. We determine the optimal PI strategy in a setting where gap risk may occur, due to downward jumps in the asset price dynamics. We consider a loss-averse agent who aims at maximizing the expected utility of the terminal wealth exceeding a minimum guarantee. We address the optimization problem via a generalization of the martingale approach that turns to be valid under market incompleteness in a jump-diffusion framework. This talk is partly based on joint works with Immacolata Oliva and Daniele Mancinelli.
Area: CS6 - Stochastic optimal control, BSDEs, and applications (Fulvia Confortola and Alessandro Calvia)
Keywords: Stochastic control, Jump diffusion processes, Portfolio Insurance strategies
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