The COVID-19 pandemic has brought legal challenges to the containment measures adopted by European countries.During the outbreak and containment phase of the pandemic,most European countries adopted measures such as l...The COVID-19 pandemic has brought legal challenges to the containment measures adopted by European countries.During the outbreak and containment phase of the pandemic,most European countries adopted measures such as lockdowns and mandatory home quarantines based on the principle of risk prevention.However,Article 15 of the European Convention on Human Rights and judgments by the European Court of Human Rights require such measures to comply with the principle of proportionality.In view of this,this article examines the European Court of Justice’s loose judgments on the derogation measures during the pandemic,and the European Court of Human Rights’situational judgments in this regard.Based on the analysis of the legitimacy of the principle of risk prevention and the principle of proportionality in responding to public health emergencies,this article prudently examines and predicts the trend of applying the principle of proportionality of risk prevention for the European COVID-19 derogation measures from three perspectives of legitimacy,necessity,and feasibility.展开更多
In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The loga...In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.展开更多
Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing num...Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.展开更多
The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk. The dynamic measure of risk to an investor in a financial market can be studied in our framewor...The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk. The dynamic measure of risk to an investor in a financial market can be studied in our framework where the wealth equation may have nonlinear coefficients.展开更多
The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance co...The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.展开更多
In this paper,we study several asymptotic behaviors of the estimators of convex and coherent entropic risk measures.First,the moderate deviation principles of the estimators are given.Second,the central limit theorems...In this paper,we study several asymptotic behaviors of the estimators of convex and coherent entropic risk measures.First,the moderate deviation principles of the estimators are given.Second,the central limit theorems of the estimators are given.Finally,several simulation results are given to support our main conclusions.展开更多
Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and varianc...Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev＇s inequality and the Khinchine＇s Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given.展开更多
This paper discusses optimal reinsurance strategy by minimizing insurer's risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected v...This paper discusses optimal reinsurance strategy by minimizing insurer's risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer's optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.展开更多
发电量的多期投标组合是一个动态的优化问题,决策过程中常常呈现多期风险,因而对风险的度量也应该是动态的。条件风险价值(conditional value at risk,CVaR)是一种静态一致性风险度量,不适用于对发电量的时间分解进行多期风险评估。该...发电量的多期投标组合是一个动态的优化问题,决策过程中常常呈现多期风险,因而对风险的度量也应该是动态的。条件风险价值(conditional value at risk,CVaR)是一种静态一致性风险度量,不适用于对发电量的时间分解进行多期风险评估。该文提出一种动态一致性风险度量,考虑风险对未来投资收益波动的长期影响,将分位数作用于静态一致性风险度量来表征多期风险的动态特征,并采用分位数回归的方法,以各期CVaR的绝对偏差加权和最小为目标函数建立数学模型,该模型可同时应用于计及风险的发电量时间分解和空间分配计算。以水电厂短期优化调度为例,说明该风险度量指标的可行性和实用性。展开更多
基金the National Social Science Fund of China’s major project“Research on Legislation and Categorization in Emergencies”(20&ZD175)the National Social Science Fund of China’s project“Research on the Relationship between Constitution and International Law”(18BFX034)
文摘The COVID-19 pandemic has brought legal challenges to the containment measures adopted by European countries.During the outbreak and containment phase of the pandemic,most European countries adopted measures such as lockdowns and mandatory home quarantines based on the principle of risk prevention.However,Article 15 of the European Convention on Human Rights and judgments by the European Court of Human Rights require such measures to comply with the principle of proportionality.In view of this,this article examines the European Court of Justice’s loose judgments on the derogation measures during the pandemic,and the European Court of Human Rights’situational judgments in this regard.Based on the analysis of the legitimacy of the principle of risk prevention and the principle of proportionality in responding to public health emergencies,this article prudently examines and predicts the trend of applying the principle of proportionality of risk prevention for the European COVID-19 derogation measures from three perspectives of legitimacy,necessity,and feasibility.
基金The NSF(10971081,11001105,11071126,10926156,11071269,J0730101)of ChinaSpecialized Research Fund(20070183023)for the Doctoral Program of Higher Education+2 种基金Program(NCET-08-237)for New Century Excellent Talents in UniversityScientific Research Fund(200810024,200903278)of Jilin University985 project of Jilin University
文摘In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.
文摘Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.
基金the National Basic Research Program of China (973 Program, No. 2007CB814900)the Natural Science Foundation of China (10671112)+1 种基金Shandong Province (Z2006A01)the New Century Excellent Young Teachers Program of Education Ministry of China
文摘The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk. The dynamic measure of risk to an investor in a financial market can be studied in our framework where the wealth equation may have nonlinear coefficients.
文摘The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.
基金supported by the National Natural Science Foundation of China(Nos.11701502,71971190).
文摘In this paper,we study several asymptotic behaviors of the estimators of convex and coherent entropic risk measures.First,the moderate deviation principles of the estimators are given.Second,the central limit theorems of the estimators are given.Finally,several simulation results are given to support our main conclusions.
基金supported by the National Natural Science Foundation of China(Grant No.60573069)the Natural Science Foundation of Hebei Province(Grant No.F2004000129)+1 种基金the Key Scientific Research Project of Hebei Education Department(Grant No.2005001D)the Key Scientific and Technical Research Project of the Ministry of Education of China(Grant No.20602).
文摘Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev＇s inequality and the Khinchine＇s Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given.
基金Zheng's research was supported by the Program of National Natural Science Foundation of Youth of China under Grant No.11201012 and PHR201007125Yang's research was supported by the Key Program of National Natural Science Foundation of China under Grant No.11131002the National Natural Science Foundation of China under Grant No.11271033
文摘This paper discusses optimal reinsurance strategy by minimizing insurer's risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer's optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.
文摘发电量的多期投标组合是一个动态的优化问题,决策过程中常常呈现多期风险,因而对风险的度量也应该是动态的。条件风险价值(conditional value at risk,CVaR)是一种静态一致性风险度量,不适用于对发电量的时间分解进行多期风险评估。该文提出一种动态一致性风险度量,考虑风险对未来投资收益波动的长期影响,将分位数作用于静态一致性风险度量来表征多期风险的动态特征,并采用分位数回归的方法,以各期CVaR的绝对偏差加权和最小为目标函数建立数学模型,该模型可同时应用于计及风险的发电量时间分解和空间分配计算。以水电厂短期优化调度为例,说明该风险度量指标的可行性和实用性。
