考虑标号 1 和 2 的两个保险公司的最优合并时刻问题. 参考文献 [3] 中模型的建立方法, 我们用漂移 Brown 运动模拟公司的风险过程, 它们的盈余过程为 dR 1 (t) = µ 1 dt + σ 1 dW 1 (t), t 0, dR 2 (t) = µ 2 dt + σ 2 dW 2 (t), t 0, 其中 µ 1 > 0 和 µ 2 > 0 是漂移系数, σ 1 和 σ 2 是波动系数. 公司 i (i = 1, 2) 的破产时刻为 τ i,0. 记合并时刻为 T. 合并后, 存在一个合并公司, 记为 m. 参考文献 [1], 我们可知公司合并通过股权 转换实现, 所以, 公司在合并过程中能避免大的融资压力和大规模现金流动. 因而, 公司的经营连续性 和稳定性不会受到影响. 类似于文献 [3], 假设合并后的公司也服从漂移 Brown 运动, 其漂移系数为 µ m , 波动系数为 σ m , 则合并后公司的盈余过程为 dR m (t) = µ m dt + σ m dW (t), t T, 其中 W (t) 是 (Ω, F, (F t) t 0 , P) 上的 Brown 运动. 由文献 [2] 知, 合并会产生固定费用, 所以, 本文 接下来假设合并发生时有一个固定费用 I 0. 又因为公司合并一般能增加公司效益, 降低其经营风 险, 参考文献 [3] 中的提法, 本文假设合并前后的漂移系数和波动系数满足 µ m µ 1 + µ 2 和 σ 2 m σ 2 1 + σ 2 2 + 2ρσ 2 1 σ 2 2 .

Group testing (or pool testing), for example, Dorfman’s method or grid method, has been validated for COVID-19 RT-PCR tests and implemented widely by most laboratories in many countries. These methods take advantages since they reduce resources, time, and overall costs required for a large number of samples. However, these methods could have more false negative cases and lower sensitivity. In order to maintain both accuracy and efficiency for different prevalence, we provide a novel pooling strategy based on the grid method with an extra pool set and an optimized rule inspired by the idea of error-correcting codes. The mathematical analysis shows that (i) the proposed method has the best sensitivity among all the methods we compared, if the false negative rate (FNR) of an individual test is in the range [1%, 20%] and the FNR of a pool test is closed to that of an individual test, and (ii) the proposed method is efficient when the prevalence is below 10%. Numerical simulations are also performed to confirm the theoretical derivations. In summary, the proposed method is shown to be felicitous under the above conditions in the epidemic.

This paper studies the on-line choice number of complete multipartite graphs with independence number m. We give a unified strategy for every prescribed m. Our main result leads to several interesting consequences comparable to known results. (1) If k 1 − *

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In this paper, we revisit the classic optimal dividend problem in a diffusion model. Note that, the aggregated dividend payments process is a càdlàg process, whose path can be partitioned into two parts: Continuous part and discontinuous part. Therefore, we incorporate both the continuous dividend form and the impulse dividend form in our model, which leads to a regular-impulse combined stochastic control problem. We assume that there exist a maximum rate for continuous dividend payments and both proportional and fixed costs for impulse dividend payments. When the company's surplus is described by a drifted Brownian motion, and the objective is to maximize the expectation of total discounted dividend payments up to the time of ruin, we obtain the explicit closed-form expressions for the value function and the optimal dividend policy. The optimal dividend policy is shown to be a combinational form of the threshold policy and the impulse policy.