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a b s t r a c tIn this paper, we consider a dual risk process which can be used to model the surplus of a business that invests money constantly and earns gains randomly in both time and amount. The occurrences of the gains and their amounts are assumed follow a semiMarkovian structure (e.g. Reinhard, 1984). We analyze a quantity resembling the Gerber-Shiu expected discounted penalty function (Gerber and Shiu, 1998) that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon exponential distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time containing the time of ruin are given along with some numerical examples.

In this paper, we study a continuous-time bivariate risk process in which each individual line of business implements a dividend barrier strategy. The insurance portfolios of the two insurers are correlated as they are subject to common shocks that induce dependent claims. To analyse the expected discounted dividends until the joint ruin time of the bivariate process (i.e. exit from the positive quadrant), we propose a discrete-time counterpart of the model and apply a bivariate extension of the Dickson−Waters discretisation with the use of a bivariate Panjer-type recursion. Detailed numerical examples under different dependencies via common shocks, copulas and proportional reinsurance are discussed, and applications to optimal problems in reinsurance, capital allocation and dividends are given. It is also illustrated that the optimal pair of dividend barriers maximising the dividend function is dependent on the initial surplus levels. A modified type of dividend barrier strategy is proposed towards the end.

Terahertz technology has its unique advantages in the field of biomedicine and is increasingly used in modern medical applications. In this study, to research the responding of biological tissues (cells or nerve nuclei) to various terahertz energy stimulation, an automatic terahertz energy control optical system is designed. The ray tracing simulation of the selfdesigned optical lens model is conducted and the results show that the system can achieve the focusing arrangement within 90 mm and control the strength of terahertz energy on image plane. In addition, an automatic control system with nanometer-level precision is designed using a stepper motor subdivision scheme to coordinate with the image plane (target point) energy and morphology adjustment. Then biomedical experiments based on this system are carried out. Through adjusting the system, terahertz intensity on cells is changed, so that the cells show various cell viabilities. The optimized experimental results show that the terahertz energy automatic control optical system designed in this study is qualified for terahertz energy irradiation research with biological cells.

The ocean is one of the most extensive ecosystems on Earth and can absorb large amounts of carbon dioxide. Changes in seawater carbon dioxide concentrations are one of the most important factors affecting marine ecosystems. Excess carbon dioxide can lead to ocean acidification, threatening the stability of marine ecosystems and species diversity. Dissolved carbon dioxide detection in seawater has great scientific significance. Conducting online monitoring of seawater carbon dioxide can help to understand the health status of marine ecosystems and to protect marine ecosystems. Current seawater detection equipment is large and costly. This study designed a low-cost infrared carbon dioxide detection system based on molecular theory. Using the HITRAN database, the absorption spectra and coefficients of carbon dioxide molecules under different conditions were calculated and derived, and a wavelength of 2361 cm−1 was selected as the measurement channel for carbon dioxide. In addition, considering the interference effect of direct light, an infrared post-splitting method was proposed to eliminate the interference of light and improve the detection accuracy of the system. The system was designed for the online monitoring of carbon dioxide in seawater, including a peristaltic pump to accelerate gas–liquid separation, an optical path structure, and carbon dioxide concentration inversion. The experimental results showed that the standard deviation of the gas test is 3.05, the standard deviation of the seawater test is 6.04, and the error range is within 20 ppm. The system can be flexibly deployed and has good stability and portability, which can meet the needs of the online monitoring of seawater carbon dioxide concentration.