In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytical...In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.展开更多
In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). ...In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.展开更多
In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation re...In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.展开更多
In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan (2009) and Karoui (2009). and the corresponding represen- measures are extens...In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan (2009) and Karoui (2009). and the corresponding represen- measures are extensions of those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
The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,thi...The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,this method not only considers the non-normality of data and information about sample size,but also meets the requirement of increasing the minimal capital ratio in BaselⅢ,basically.The authors theoretically prove the translation invariance,monotonicity and subadditivity of MMVaR as a risk measure under some conditions,and study its finite sample properties through Monte Carlo simulations.The empirical analysis shows that MMVaR can measure multi-period risk accurately.展开更多
Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing conc...Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing concern of the community.In this paper we present a novel credit risk measurement method based on a dimensional reduation technique.The method first extracts the risk measure indexes from the basal financial data via dimensional reduation by using deep belief network(DBN),exploratory factor analysis(EFA)and confirmatory factor analysis(CFA)in turn.And then the credit risk is measured by a systemic structural equation model(SEM)and logistic distribution.To validate the proposed method,we employ the financial data of the listed companies from Q12019 to Q22022.The empirical results show its effectiveness on statistical evaluation,assessment on testing samples and credit risk forecasting.展开更多
We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attit...We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.展开更多
Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example t...Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example to analyze deep foundation pit excavation technology,including the nature of this construction project,the main technical measures in the construction of deep foundation pit,and the analysis of the safety risk prevention and control measures.The purpose of this analysis is to provide scientific reference for the construction quality and safety of deep foundation pits.展开更多
In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-...In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.展开更多
G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,a...G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.展开更多
In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncer...In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.展开更多
Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in math...Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.展开更多
This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment...This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment analysis(DEA). The derived model serves as an input-oriented DEA model by minimizing inputs such as multiple risk measures. In addition, the Russell input measure is introduced and the corresponding efficiency results are evaluated. The findings show that stock efficiency evaluation under the new framework is also effective. The efficiency values indicate that the portfolio frontier under the new framework is more externally enveloped than the DEA efficient surface under the standard DEA framework.展开更多
This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distorti...This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.展开更多
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time setup.The two key operational concepts used throughout are the no...In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time setup.The two key operational concepts used throughout are the notion of the LMmeasure and the notion of the update rule that,we believe,are the key tools for studying time consistency in a unified framework.展开更多
For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we i...For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.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
This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of ...This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.展开更多
This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity ...This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity aversion yields a higher value for VaR and Expected Shortfall(ES),the result can be reversed in a deeply ambiguous environment.Additionally,some sufficient conditions are provided for the preservation of this effect under various forms of risk aggregation.This study offers a new perspective to full awareness on capital requirement calculation as requested by international regulation.展开更多
基金supported by the National Natural Science Foundation of China (11901184, 11771343)the Natural Science Foundation of Hunan Province (2020JJ5025)。
文摘In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.
基金Supported by the National Natural Science Foundation of China(11371284)the Natural Science Foundation of Henan Province(14B110037)
文摘In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.
基金Supported by the National Natural Science Foundation of China(11371284,11771343)
文摘In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.
基金Supported in part by the National Natural Science Foundation of China (10971157)Key Projects of Philosophy and Social Sciences Research+1 种基金Ministry of Education of China (09JZD0027)The Talent Introduction Projects of Nanjing Audit University
文摘In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan (2009) and Karoui (2009). and the corresponding represen- measures are extensions of those
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.
基金supported by the National Social Science Fund of China under Grant No.22BTJ027。
文摘The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,this method not only considers the non-normality of data and information about sample size,but also meets the requirement of increasing the minimal capital ratio in BaselⅢ,basically.The authors theoretically prove the translation invariance,monotonicity and subadditivity of MMVaR as a risk measure under some conditions,and study its finite sample properties through Monte Carlo simulations.The empirical analysis shows that MMVaR can measure multi-period risk accurately.
基金Supported by the National Social Science Foundation of China(21CTJ005)the Anhui Provincial Natural Science Foundation(KJ2017A105)。
文摘Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing concern of the community.In this paper we present a novel credit risk measurement method based on a dimensional reduation technique.The method first extracts the risk measure indexes from the basal financial data via dimensional reduation by using deep belief network(DBN),exploratory factor analysis(EFA)and confirmatory factor analysis(CFA)in turn.And then the credit risk is measured by a systemic structural equation model(SEM)and logistic distribution.To validate the proposed method,we employ the financial data of the listed companies from Q12019 to Q22022.The empirical results show its effectiveness on statistical evaluation,assessment on testing samples and credit risk forecasting.
文摘We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.
文摘Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example to analyze deep foundation pit excavation technology,including the nature of this construction project,the main technical measures in the construction of deep foundation pit,and the analysis of the safety risk prevention and control measures.The purpose of this analysis is to provide scientific reference for the construction quality and safety of deep foundation pits.
基金supported by the Important Natural Science Foundation of Colleges and Universities of Anhui Province under Grant No.KJ2020A0122the Scientific Research Start-up Foundation of Hefei Normal University。
文摘In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.
基金supported by Natural Science Foundation of China and Jiangsu Province(No.11871050,No.11971342,No.11401414,No.BK20140299,No.14KJB110022)。
文摘G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.
基金This research was supported by the National Natural Science Foundation of China(Nos.71371152 and 11571270).
文摘In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.
基金the support from the Natural Sciences and Engineering Research Council of Canada(NSERC)(grant No.RGPIN-2016-03975)supported by grants from the National Natural Science Foundation of China(Grant No.11971505)111 Project of China(No.B17050).
文摘Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.
基金supported by the National Natural Science Foundation of China under Grant Nos.72071192,71671172the Anhui Provincial Quality Engineering Teaching and Research Project Under Grant No.2020jyxm2279+2 种基金the Anhui University and Enterprise Cooperation Practice Education Base Project under Grant No.2019sjjd02Teaching and Research Project of USTC(2019xjyxm019,2020ycjg08)the Fundamental Research Funds for the Central Universities(WK2040000027)。
文摘This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment analysis(DEA). The derived model serves as an input-oriented DEA model by minimizing inputs such as multiple risk measures. In addition, the Russell input measure is introduced and the corresponding efficiency results are evaluated. The findings show that stock efficiency evaluation under the new framework is also effective. The efficiency values indicate that the portfolio frontier under the new framework is more externally enveloped than the DEA efficient surface under the standard DEA framework.
文摘This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.
基金Tomasz R.Bielecki and Igor Cialenco acknowledge support from the NSF grant DMS-1211256.Part of the research was performed while Igor Cialenco was visiting the Institute for Pure and Applied Mathematics(IPAM),which is supported by the National Science Foundation.Marcin Pitera acknowledges the support by Project operated within the Foundation for Polish Science IPP Programme“Geometry and Topology in Physical Model”co-financed by the EU European Regional Development Fund,Operational Program Innovative Economy 2007–2013.
文摘In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time setup.The two key operational concepts used throughout are the notion of the LMmeasure and the notion of the update rule that,we believe,are the key tools for studying time consistency in a unified framework.
基金supported by the National Key Research and Development Plan(No.2016YFC0800100)the NSFC of China(Nos.11671374,71771203,71631006).
文摘For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.
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.
文摘This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.
文摘This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity aversion yields a higher value for VaR and Expected Shortfall(ES),the result can be reversed in a deeply ambiguous environment.Additionally,some sufficient conditions are provided for the preservation of this effect under various forms of risk aggregation.This study offers a new perspective to full awareness on capital requirement calculation as requested by international regulation.