In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and the...In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.展开更多
Finding the optimal dose combination in two-agent dose-finding trials is challenging due to limited sample sizes and the extensive range of potential doses.Unlike traditional chemotherapy or radiotherapy,which primari...Finding the optimal dose combination in two-agent dose-finding trials is challenging due to limited sample sizes and the extensive range of potential doses.Unlike traditional chemotherapy or radiotherapy,which primarily focuses on identifying the maximum tolerated dose(MTD),therapies involving targeted and immune agents facilitate the identifica-tion of an optimal biological dose combination(OBDC)by simultaneously evaluating both toxicity and efficacy.Cur-rently,most approaches to determining the OBDC in the literature are model-based and require complex model fittings,making them cumbersome and challenging to implement.To address these challenges,we developed a novel model-as-sisted approach called uTPI-Comb.This approach refines the established utility-based toxicity probability interval design by integrating a strategically devised zone-based local and global candidate set searching strategy,which can effectively optimize the decision-making process for two-agent dose escalation or de-escalation in drug combination trials.Extensive simulation studies demonstrate that the uTPI-Comb design speeds up the dose-searching process and provides substantial improvements over existing model-based methods in determining the optimal biological dose combinations.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12301603).
文摘In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.
基金This work was supported by the Natural Science Foundation of Anhui Province(2022AH050703)the National Natural Science Foundation of China(11671375).
文摘Finding the optimal dose combination in two-agent dose-finding trials is challenging due to limited sample sizes and the extensive range of potential doses.Unlike traditional chemotherapy or radiotherapy,which primarily focuses on identifying the maximum tolerated dose(MTD),therapies involving targeted and immune agents facilitate the identifica-tion of an optimal biological dose combination(OBDC)by simultaneously evaluating both toxicity and efficacy.Cur-rently,most approaches to determining the OBDC in the literature are model-based and require complex model fittings,making them cumbersome and challenging to implement.To address these challenges,we developed a novel model-as-sisted approach called uTPI-Comb.This approach refines the established utility-based toxicity probability interval design by integrating a strategically devised zone-based local and global candidate set searching strategy,which can effectively optimize the decision-making process for two-agent dose escalation or de-escalation in drug combination trials.Extensive simulation studies demonstrate that the uTPI-Comb design speeds up the dose-searching process and provides substantial improvements over existing model-based methods in determining the optimal biological dose combinations.
