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
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
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 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, 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
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
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
This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future un...This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.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
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 construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic r...In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.展开更多
Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric meth...Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.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
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
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
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 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
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
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
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.
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.
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 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 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.
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.
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This study was funded by the MITACS Accelerate Grant-Award Number IT12339the Foreign Young Talents Program of the Ministry of Science and Technology of China(QN20200017001)the China Postdoctoral Science Foundation(2020M672913).
文摘This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.
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Supported by National Natural Science Foundation of China(11301461)Natural Science Foundation of Jiangsu Province(BK20130435)University Natural Science Foundation of Jiangsu Province(13KJB110031)
文摘In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.
文摘Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.
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 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.
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.
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.
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.