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AbstractIn this article, we analyze a robust optimal reinsurance and investment problem in a model with default risks and jumps for a general company which holds shares of an insurer and a reinsurer. The insurer’s surplus is characterized by a diffusion model and the insurer has the opportunity to buy proportional reinsurance from the reinsurer. Moreover, the insurer can invest in a risk-free asset (bank account), a risky asset (stock), and a defaultable bond. Meanwhile, the reinsurer can also invest in a risk-free asset and another risky asset. The price dynamics of the risky asset is assumed to follow a jump-diffusion model. What is more, the general company is concerned about the ambiguity and aims to find a robust optimal reinsurance and investment strategy. The objective of the general company is to maximize the minimal expected exponential utility of the weighted sums of the insurer’s and the reinsurer’s terminal wealth. Applying stochastic dynamic programming approach, we first establish the robust HJB (Hamilton-Jacobi-Bellman) equations for the post-default case and the pre-default case, respectively. Furthermore, we obtain the robust optimal strategy explicitly and present the corresponding verification theorem. Finally, we give some numerical examples to demonstrate the influences of model parameters on the robust optimal strategy. [ABSTRACT FROM AUTHOR]

TiO2, molecularly imprinted TiO2(TiO2/OTC) and a novel Si doped molecularly imprinted TiO2(TiO2/SiO2/OTC) nano photocatalytic materials were prepared by liquid phase deposition method. The products were characterized by XRD and SEM. The photocatalytic activities of the samples were evaluated by the photocatalytic degradation of oxytetracycline wastewater under a xenon lamp irradiation. The results showed that TiO2/SiO2/OTC and TiO2/OTC could improve both the photocatalytic activity and the molecular recognition ability, while the photocatalytic activities of TiO2/SiO2/OTC sample was more effective than TiO2/OTC sample with 5 times reuse. The photocatalytic activity of TiO2/SiO2/OTC photocatalyst sample had a greater improvement and its photocatalytic degradation of oxytetracycline wastewater reached 80.79% in 120 minute reaction. [ABSTRACT FROM PUBLISHER]

In this paper, we study a discrete susceptible-infected-removed epidemic model with vaccination and treatment and it is shown that the global dynamics is determined by the basic reproduction number. If, then the disease-free equilibrium is globally asymptotically stable and if, then the endemic equilibrium is globally asymptotically stable. [ABSTRACT FROM PUBLISHER]

An non-standard finite difference scheme is employed to discuss a class of SIR epidemic model with vaccination and treatment. The dynamical properties of the discretized model are then analysed. The results demonstrate that the discretized epidemic model is dynamically consistent with the continuous model since it maintains essential properties of the corresponding continuous model, such as positivity property and boundness of solutions, equilibrium points and their local stability properties. [ABSTRACT FROM PUBLISHER]