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
In this article,we study optimal reinsurance design.By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle,we study and obtain the optimal reinsurance ...In this article,we study optimal reinsurance design.By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle,we study and obtain the optimal reinsurance treaty by minimizing the VaR(value at risk)of the reinsurer's total risk exposure.When the distortion premium principle is specified to be the expectation premium principle,we also obtain the optimal reinsurance treaty by minimizing the CTE(conditional tail expectation)of the reinsurer's total risk exposure.The present study can be considered as a complement of that of Cai et al.[5].展开更多
In the classical credibility theory, the credibility premium is derived on the basis of pure premium. However, the insurance practice demands that the premium must be charged under some adaptable premium principle and...In the classical credibility theory, the credibility premium is derived on the basis of pure premium. However, the insurance practice demands that the premium must be charged under some adaptable premium principle and serves the purpose for insurance business. In this paper, the balanced credibility models have been built under exponential principle, and the credibility estimator of individual exponential premium is derived. This result is also extended to the versions of multitude contracts, and the estimation of the structure parameters is investigated. Finally, the simulations have been introduced to show the consistency of the credibility estimator and its differences from the classical one.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
In this paper,the authors investigate the optimal per-claim reinsurance problem under the continuous-time framework to minimize the insurer's ruin probability based on the Lundberg exponent.Considering reinsurance...In this paper,the authors investigate the optimal per-claim reinsurance problem under the continuous-time framework to minimize the insurer's ruin probability based on the Lundberg exponent.Considering reinsurance participants'diversified risk preferences,the authors assume that the reinsurance premium is calculated by a combined premium principle,including the expected value premium principle and upper moment premium principle.Then,the authors derive the insurer's optimal reinsurance strategy satisfying the principle of indemnity and the incentive compatibility condition in an infinite reinsurance space based on the point-wise optimization approach.Besides,the proposed work emphasizes the optimality and admissibility of the combination of the excess of loss reinsurance and its dual form when a piecewise reinsurance premium principle is considered.As a special case,the optimal reinsurance strategy under the expected value premium principle reduces to the classic result.Furthermore,the numerical analyses are provided to illustrate the effects of the main parameters on the maximal Lundberg exponent and the optimal reinsurance strategy.展开更多
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 Natural Science Foundation of Xinjiang Province(2018D01C074)the National Natural Science Foundation of China(11861064,11771343,61563050)。
文摘In this article,we study optimal reinsurance design.By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle,we study and obtain the optimal reinsurance treaty by minimizing the VaR(value at risk)of the reinsurer's total risk exposure.When the distortion premium principle is specified to be the expectation premium principle,we also obtain the optimal reinsurance treaty by minimizing the CTE(conditional tail expectation)of the reinsurer's total risk exposure.The present study can be considered as a complement of that of Cai et al.[5].
基金Supported by National Natural Science Foundation of China （Grant No. 71001046）, Science Foundation of the Education Department of Jiangxi （Grant No. GJJ10096）, and Scientific Funds of Jiangxi Normal University
文摘In the classical credibility theory, the credibility premium is derived on the basis of pure premium. However, the insurance practice demands that the premium must be charged under some adaptable premium principle and serves the purpose for insurance business. In this paper, the balanced credibility models have been built under exponential principle, and the credibility estimator of individual exponential premium is derived. This result is also extended to the versions of multitude contracts, and the estimation of the structure parameters is investigated. Finally, the simulations have been introduced to show the consistency of the credibility estimator and its differences from the classical one.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.12071498 and 12371478the Program for Innovation Research in Central University of Finance and Economics and Innovation Introduction Base for Insurance Risk Analysis and Decision Making Discipline under Grant No.B17050。
文摘In this paper,the authors investigate the optimal per-claim reinsurance problem under the continuous-time framework to minimize the insurer's ruin probability based on the Lundberg exponent.Considering reinsurance participants'diversified risk preferences,the authors assume that the reinsurance premium is calculated by a combined premium principle,including the expected value premium principle and upper moment premium principle.Then,the authors derive the insurer's optimal reinsurance strategy satisfying the principle of indemnity and the incentive compatibility condition in an infinite reinsurance space based on the point-wise optimization approach.Besides,the proposed work emphasizes the optimality and admissibility of the combination of the excess of loss reinsurance and its dual form when a piecewise reinsurance premium principle is considered.As a special case,the optimal reinsurance strategy under the expected value premium principle reduces to the classic result.Furthermore,the numerical analyses are provided to illustrate the effects of the main parameters on the maximal Lundberg exponent and the optimal reinsurance strategy.
