Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump

In this paper, we investigate the sufficient conditions for null controllability of noninstantaneous impulsive Hilfer fractional stochastic integrodifferential system with the Rosenblatt process and Poisson jump. The required results are obtained based on fractional calculus, stochastic analysis, and Sadovskii’s fixed point theorem. Finally, an example is given to illustrate the obtained results.

Pricing of Power Exchange Option with Jumps under the Double Risk of Exchange and Default

Power exchange option is an exotic option which combines power option and exchange option. In this paper, we consider the pricing of the power exchange option under exchange rate volatility risk and issuing company bankruptcy risk. Meanwhile, considering the major events between the two countries, we add the Poisson jump process to the option model in order to reflect the impact of sudden factors on the price of transnational derivatives in the international market. According to the no-arbitrage principle, a mathematical model for pricing such problems is established, and explicit solutions are obtained. The numerical examples show that the model established in this paper is effective.

Exponential stability for neutral stochastic partial integro-differential equations of second order with poisson jumps

This paper studies the existence, uniqueness and the exponential stability in p-th moment of the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. The existence and uniqueness of the mild solution of neutral second order stochastic differential equation is first established by means of Banach fixed point principle and stochastic analysis. The exponential stability in the p-th moment for the mild solution to impulsive neutral stochastic integrodifferential equations with Poisson jump is obtained by establishing an integral inequality.