This paper aims to value the cliquet-style equity-linked insurance product with death benefits. Whether insured dies before contract maturity or not, a benefit payment beneficiary is due. The premium invested in financial asset, whose dynamics are assumed follow an exponential jump diffusion. In addition, remaining lifetime of modelled by independent random variable distribution can be approxim...

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump–diffusion in which both the diffusion and jump amplitude are log– normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The ju...

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump–diffusion in which both the diffusion and jump amplitude are log–normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The jum...

We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we provide a pathwise result that shows that the considered process converges to an advection-diffusion process in the (long-time) diffusion limit. We also (re...

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models where conditional returns are constrained to being normal, as well as extends Merton’s jump-diffusion model by allowing return volatility to exhibit GARCH-like behavior. Empirical analysis on the S&P 500 index r...