Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the E...Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.展开更多
In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with...In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.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, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heu...In this paper, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heuristic device generating compositional scenarios, based on information theory concepts, namely weighted entropy. New proofs concerning the maximum value of the index and the evaluation of optimal proportions are outlined, with emphasis on the optimal value of the Lagrange multiplier and its meaning. The rationale is a procedure of maximizing the combined value of a system expressed as a mosaic, denoted by characteristic values of the states and their proportions. Other perspectives of application of this EU-WE framework are suggested.展开更多
Conjunction of two probability laws can give rise to a possibility law. Using two probability densities over two disjoint ranges, we can define the fuzzy mean of a fuzzy variable with the help of means two random vari...Conjunction of two probability laws can give rise to a possibility law. Using two probability densities over two disjoint ranges, we can define the fuzzy mean of a fuzzy variable with the help of means two random variables in two disjoint spaces.展开更多
In recent years,China has accelerated the reform of its oil and gas management system,especially in competitive transfer of mining rights.Evaluating the expected value(EV)of lease blocks is crucial for the bidding dec...In recent years,China has accelerated the reform of its oil and gas management system,especially in competitive transfer of mining rights.Evaluating the expected value(EV)of lease blocks is crucial for the bidding decision of oil companies.When bidding for a block with several individual prospects,the simple addition of each prospect EV usually leads to overly high and optimistic resource volume and value estimates.For the assessment of the EV of a multi-prospect block,two factors should be considered.Firstly,the geological setting of the prospects,including their relative spatial relationship,their chance of geological success,their resources and their geological dependency,etc.The second factor is the exploration strategy of oil companies,concerned with the dry hole tolerance,the committed wells and the drilling priorities for the prospects,etc.A probabilistic method to assess the EV of a multi-prospect block is proposed,which proves to be favorable for formulating a bidding strategy for oil companies.In addition,a case study on two specific blocks with several prospects is presented to illustrate the effect of the above mentioned factors on the EV.展开更多
This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market in...This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.展开更多
文摘Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.
基金The NSF (11201217) of Chinathe NSF (20132BAB211010) of Jiangxi Province
文摘In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.
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.
文摘In this paper, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heuristic device generating compositional scenarios, based on information theory concepts, namely weighted entropy. New proofs concerning the maximum value of the index and the evaluation of optimal proportions are outlined, with emphasis on the optimal value of the Lagrange multiplier and its meaning. The rationale is a procedure of maximizing the combined value of a system expressed as a mosaic, denoted by characteristic values of the states and their proportions. Other perspectives of application of this EU-WE framework are suggested.
文摘Conjunction of two probability laws can give rise to a possibility law. Using two probability densities over two disjoint ranges, we can define the fuzzy mean of a fuzzy variable with the help of means two random variables in two disjoint spaces.
基金Sinopec Science and Technology Research Project"Evaluation and Decision Support Technology for Oil and Gas Strategic Area Selection"(P21086-1).
文摘In recent years,China has accelerated the reform of its oil and gas management system,especially in competitive transfer of mining rights.Evaluating the expected value(EV)of lease blocks is crucial for the bidding decision of oil companies.When bidding for a block with several individual prospects,the simple addition of each prospect EV usually leads to overly high and optimistic resource volume and value estimates.For the assessment of the EV of a multi-prospect block,two factors should be considered.Firstly,the geological setting of the prospects,including their relative spatial relationship,their chance of geological success,their resources and their geological dependency,etc.The second factor is the exploration strategy of oil companies,concerned with the dry hole tolerance,the committed wells and the drilling priorities for the prospects,etc.A probabilistic method to assess the EV of a multi-prospect block is proposed,which proves to be favorable for formulating a bidding strategy for oil companies.In addition,a case study on two specific blocks with several prospects is presented to illustrate the effect of the above mentioned factors on the EV.
文摘This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.
