ABSTRACT This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.
{"title":"OPTIMAL REINSURANCE DESIGN WITH DISTORTION RISK MEASURES AND ASYMMETRIC INFORMATION","authors":"T. Boonen, Yiying Zhang","doi":"10.1017/asb.2021.8","DOIUrl":"https://doi.org/10.1017/asb.2021.8","url":null,"abstract":"ABSTRACT This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"19 1","pages":"607 - 629"},"PeriodicalIF":1.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79300886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT Target date funds (TDFs) are becoming increasingly popular investment choices among investors with long-term prospects. Examples include members of superannuation funds seeking to save for retirement at a given age. TDFs provide efficient risk exposures to a diversified range of asset classes that dynamically match the risk profile of the investment payoff as the investors age. This is often achieved by making increasingly conservative asset allocations over time as the retirement date approaches. Such dynamically evolving allocation strategies for TDFs are often referred to as glide paths. We propose a systematic approach to the design of optimal TDF glide paths implied by retirement dates and risk preferences and construct the corresponding dynamic asset allocation strategy that delivers the optimal payoffs at minimal costs. The TDF strategies we propose are dynamic portfolios consisting of units of the growth-optimal portfolio (GP) and the risk-free asset. Here, the GP is often approximated by a well-diversified index of multiple risky assets. We backtest the TDF strategies with the historical returns of the S&P500 total return index serving as the GP approximation.
{"title":"DYNAMIC ASSET ALLOCATION FOR TARGET DATE FUNDS UNDER THE BENCHMARK APPROACH","authors":"Jin Sun, Dan Zhu, E. Platen","doi":"10.1017/asb.2021.6","DOIUrl":"https://doi.org/10.1017/asb.2021.6","url":null,"abstract":"ABSTRACT Target date funds (TDFs) are becoming increasingly popular investment choices among investors with long-term prospects. Examples include members of superannuation funds seeking to save for retirement at a given age. TDFs provide efficient risk exposures to a diversified range of asset classes that dynamically match the risk profile of the investment payoff as the investors age. This is often achieved by making increasingly conservative asset allocations over time as the retirement date approaches. Such dynamically evolving allocation strategies for TDFs are often referred to as glide paths. We propose a systematic approach to the design of optimal TDF glide paths implied by retirement dates and risk preferences and construct the corresponding dynamic asset allocation strategy that delivers the optimal payoffs at minimal costs. The TDF strategies we propose are dynamic portfolios consisting of units of the growth-optimal portfolio (GP) and the risk-free asset. Here, the GP is often approximated by a well-diversified index of multiple risky assets. We backtest the TDF strategies with the historical returns of the S&P500 total return index serving as the GP approximation.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"213 1","pages":"449 - 474"},"PeriodicalIF":1.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77597423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.
{"title":"OPTIMAL INCENTIVE-COMPATIBLE INSURANCE WITH BACKGROUND RISK","authors":"Yichun Chi, K. S. Tan","doi":"10.1017/asb.2021.7","DOIUrl":"https://doi.org/10.1017/asb.2021.7","url":null,"abstract":"ABSTRACT In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"11 1","pages":"661 - 688"},"PeriodicalIF":1.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89816737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT Even though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.
{"title":"PRICING LONGEVITY-LINKED SECURITIES IN THE PRESENCE OF MORTALITY TREND CHANGES","authors":"Arne Freimann","doi":"10.1017/asb.2021.5","DOIUrl":"https://doi.org/10.1017/asb.2021.5","url":null,"abstract":"ABSTRACT Even though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"33 1","pages":"411 - 447"},"PeriodicalIF":1.9,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74485306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The primary objective of this scholarly work is to develop two estimation procedures – maximum likelihood estimator (MLE) and method of trimmed moments (MTM) – for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.
{"title":"ROBUST ESTIMATION OF LOSS MODELS FOR LOGNORMAL INSURANCE PAYMENT SEVERITY DATA","authors":"Chudamani Poudyal","doi":"10.1017/asb.2021.4","DOIUrl":"https://doi.org/10.1017/asb.2021.4","url":null,"abstract":"Abstract The primary objective of this scholarly work is to develop two estimation procedures – maximum likelihood estimator (MLE) and method of trimmed moments (MTM) – for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"199 1","pages":"475 - 507"},"PeriodicalIF":1.9,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88980325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dilan SriDaran, M. Sherris, Andrés M. Villegas, Jonathan Ziveyi
Abstract Given the rapid reductions in human mortality observed over recent decades and the uncertainty associated with their future evolution, there have been a large number of mortality projection models proposed by actuaries and demographers in recent years. Many of these, however, suffer from being overly complex, thereby producing spurious forecasts, particularly over long horizons and for small, noisy data sets. In this paper, we exploit statistical learning tools, namely group regularisation and cross-validation, to provide a robust framework to construct discrete-time mortality models by automatically selecting the most appropriate functions to best describe and forecast particular data sets. Most importantly, this approach produces bespoke models using a trade-off between complexity (to draw as much insight as possible from limited data sets) and parsimony (to prevent over-fitting to noise), with this trade-off designed to have specific regard to the forecasting horizon of interest. This is illustrated using both empirical data from the Human Mortality Database and simulated data, using code that has been made available within a user-friendly open-source R package StMoMo.
{"title":"A GROUP REGULARISATION APPROACH FOR CONSTRUCTING GENERALISED AGE-PERIOD-COHORT MORTALITY PROJECTION MODELS","authors":"Dilan SriDaran, M. Sherris, Andrés M. Villegas, Jonathan Ziveyi","doi":"10.1017/asb.2021.29","DOIUrl":"https://doi.org/10.1017/asb.2021.29","url":null,"abstract":"Abstract Given the rapid reductions in human mortality observed over recent decades and the uncertainty associated with their future evolution, there have been a large number of mortality projection models proposed by actuaries and demographers in recent years. Many of these, however, suffer from being overly complex, thereby producing spurious forecasts, particularly over long horizons and for small, noisy data sets. In this paper, we exploit statistical learning tools, namely group regularisation and cross-validation, to provide a robust framework to construct discrete-time mortality models by automatically selecting the most appropriate functions to best describe and forecast particular data sets. Most importantly, this approach produces bespoke models using a trade-off between complexity (to draw as much insight as possible from limited data sets) and parsimony (to prevent over-fitting to noise), with this trade-off designed to have specific regard to the forecasting horizon of interest. This is illustrated using both empirical data from the Human Mortality Database and simulated data, using code that has been made available within a user-friendly open-source R package StMoMo.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"35 1","pages":"247 - 289"},"PeriodicalIF":1.9,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89449026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The Lee–Carter model has become a benchmark in stochastic mortality modeling. However, its forecasting performance can be significantly improved upon by modern machine learning techniques. We propose a convolutional neural network (NN) architecture for mortality rate forecasting, empirically compare this model as well as other NN models to the Lee–Carter model and find that lower forecast errors are achievable for many countries in the Human Mortality Database. We provide details on the errors and forecasts of our model to make it more understandable and, thus, more trustworthy. As NN by default only yield point estimates, previous works applying them to mortality modeling have not investigated prediction uncertainty. We address this gap in the literature by implementing a bootstrapping-based technique and demonstrate that it yields highly reliable prediction intervals for our NN model.
{"title":"POINT AND INTERVAL FORECASTS OF DEATH RATES USING NEURAL NETWORKS","authors":"Simon Schnürch, R. Korn","doi":"10.1017/asb.2021.34","DOIUrl":"https://doi.org/10.1017/asb.2021.34","url":null,"abstract":"Abstract The Lee–Carter model has become a benchmark in stochastic mortality modeling. However, its forecasting performance can be significantly improved upon by modern machine learning techniques. We propose a convolutional neural network (NN) architecture for mortality rate forecasting, empirically compare this model as well as other NN models to the Lee–Carter model and find that lower forecast errors are achievable for many countries in the Human Mortality Database. We provide details on the errors and forecasts of our model to make it more understandable and, thus, more trustworthy. As NN by default only yield point estimates, previous works applying them to mortality modeling have not investigated prediction uncertainty. We address this gap in the literature by implementing a bootstrapping-based technique and demonstrate that it yields highly reliable prediction intervals for our NN model.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"4 1","pages":"333 - 360"},"PeriodicalIF":1.9,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85559329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Assessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.
{"title":"ESTIMATION OF HIGH CONDITIONAL TAIL RISK BASED ON EXPECTILE REGRESSION","authors":"Jie Hu, Yu Chen, Keqi Tan","doi":"10.1017/asb.2021.3","DOIUrl":"https://doi.org/10.1017/asb.2021.3","url":null,"abstract":"Abstract Assessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"1 1","pages":"539 - 570"},"PeriodicalIF":1.9,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88470136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We construct a double common factor model for projecting the mortality of a population using as a reference the minimum death rate at each age among a large number of countries. In particular, the female and male minimum death rates, described as best-performance or best-practice rates, are first modelled by a common factor model structure with both common and sex-specific parameters. The differences between the death rates of the population under study and the best-performance rates are then modelled by another common factor model structure. An important result of using our proposed model is that the projected death rates of the population being considered are coherent with the projected best-performance rates in the long term, the latter of which serves as a very useful reference for the projection based on the collective experience of multiple countries. Our out-of-sample analysis shows that the new model has potential to outperform some conventional approaches in mortality projection.
{"title":"A DOUBLE COMMON FACTOR MODEL FOR MORTALITY PROJECTION USING BEST-PERFORMANCE MORTALITY RATES AS REFERENCE","authors":"Jackie Li, Maggie Lee, S. Guthrie","doi":"10.1017/asb.2020.44","DOIUrl":"https://doi.org/10.1017/asb.2020.44","url":null,"abstract":"Abstract We construct a double common factor model for projecting the mortality of a population using as a reference the minimum death rate at each age among a large number of countries. In particular, the female and male minimum death rates, described as best-performance or best-practice rates, are first modelled by a common factor model structure with both common and sex-specific parameters. The differences between the death rates of the population under study and the best-performance rates are then modelled by another common factor model structure. An important result of using our proposed model is that the projected death rates of the population being considered are coherent with the projected best-performance rates in the long term, the latter of which serves as a very useful reference for the projection based on the collective experience of multiple countries. Our out-of-sample analysis shows that the new model has potential to outperform some conventional approaches in mortality projection.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"108 1","pages":"349 - 374"},"PeriodicalIF":1.9,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76384740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable tail dependence since it evaluates the limiting tail probability only along the main diagonal. To overcome these issues, two novel tail dependence measures called the maximal tail concordance measure (MTCM) and the average tail concordance measure (ATCM) are proposed. Both measures are constructed based on tail copulas and possess clear probabilistic interpretations in that the MTCM evaluates the largest limiting probability among all comparable rectangles in the tail, and the ATCM is a normalized average of these limiting probabilities. In contrast to the TDC, the proposed measures can capture non-exchangeable tail dependence. Analytical forms of the proposed measures are also derived for various copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.
{"title":"Measuring non-exchangeable tail dependence using tail copulas","authors":"Takaaki Koike, Shogo Kato, M. Hofert","doi":"10.1017/asb.2023.4","DOIUrl":"https://doi.org/10.1017/asb.2023.4","url":null,"abstract":"Abstract Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable tail dependence since it evaluates the limiting tail probability only along the main diagonal. To overcome these issues, two novel tail dependence measures called the maximal tail concordance measure (MTCM) and the average tail concordance measure (ATCM) are proposed. Both measures are constructed based on tail copulas and possess clear probabilistic interpretations in that the MTCM evaluates the largest limiting probability among all comparable rectangles in the tail, and the ATCM is a normalized average of these limiting probabilities. In contrast to the TDC, the proposed measures can capture non-exchangeable tail dependence. Analytical forms of the proposed measures are also derived for various copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":"27 1","pages":"466 - 487"},"PeriodicalIF":1.9,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74237099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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