Pub Date : 2023-12-14DOI: 10.1080/03461238.2023.2277786
Jamaal Ahmad, Mogens Bladt
In this paper, we consider statistical estimation of time–inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi–state life insur...
{"title":"Aggregate Markov models in life insurance: estimation via the EM algorithm","authors":"Jamaal Ahmad, Mogens Bladt","doi":"10.1080/03461238.2023.2277786","DOIUrl":"https://doi.org/10.1080/03461238.2023.2277786","url":null,"abstract":"In this paper, we consider statistical estimation of time–inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi–state life insur...","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138686477","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}
Pub Date : 2023-12-06DOI: 10.1080/03461238.2023.2289372
Guohui Guan, Zongxia Liang, Yi Xia
This paper investigates the optimal management of an aggregated defined benefit pension plan in a stochastic environment. The interest rate follows the Ornstein-Uhlenbeck model, the benefits follow...
{"title":"Optimal management of DB pension fund under both underfunded and overfunded cases","authors":"Guohui Guan, Zongxia Liang, Yi Xia","doi":"10.1080/03461238.2023.2289372","DOIUrl":"https://doi.org/10.1080/03461238.2023.2289372","url":null,"abstract":"This paper investigates the optimal management of an aggregated defined benefit pension plan in a stochastic environment. The interest rate follows the Ornstein-Uhlenbeck model, the benefits follow...","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138556908","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}
Pub Date : 2023-11-16DOI: 10.1080/03461238.2023.2280287
Lucas van Kreveld, Michel Mandjes, Jan-Pieter Dorsman
This paper studies the Cramér–Lundberg asymptotics of the ruin probability for a model in which the reserve level process is described by a spectrally-positive light-tailed Markov additive process....
本文研究了用谱正光尾马尔可夫加性过程....描述储备水平过程的模型的破产概率的cram r - lundberg渐近性
{"title":"Cramér–Lundberg asymptotics for spectrally positive Markov additive processes","authors":"Lucas van Kreveld, Michel Mandjes, Jan-Pieter Dorsman","doi":"10.1080/03461238.2023.2280287","DOIUrl":"https://doi.org/10.1080/03461238.2023.2280287","url":null,"abstract":"This paper studies the Cramér–Lundberg asymptotics of the ruin probability for a model in which the reserve level process is described by a spectrally-positive light-tailed Markov additive process....","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528650","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}
Pub Date : 2023-11-13DOI: 10.1080/03461238.2023.2275276
Kaixin Yan, Shuanming Li, Aili Zhang
AbstractThis paper studies the valuation of equity-linked investment products embedded with a high-water mark (HWM) fee structure. Under the HWM fee structure, the insurance company charges threshold fees at a constant rate from the policyholder's account whenever the account value is lower than a pre-specified level, and levies HMW fees at another constant rate whenever the account is hitting new record highs that are higher than another pre-specified level. The dynamics of the logarithmic value of the policyholder's account, before fees, is assumed to follow either a two-sided jump-diffusion process with double exponential jumps, or a down-ward jump-diffusion process with exponential jumps. For the two-sided jump-diffusion model with HWM fees, using the Wiener–Hopf factorisation theorem and the duality lemma, we derive an explicit expression for its potential measure. For the down-ward jump-diffusion model with both threshold fees and HWM fees, we are facilitated with the excursion theory to derive an explicit expression of the potential measure. Using the above newly derived potential measures, we are able to obtain formulas for valuing the equity-linked annuity under the HWM fee structure. Finally, we illustrate our results with some numerical examples.KEYWORDS: Equity-linked annuityhigh-water mark fee structurejump-diffusion process AcknowledgementsThe authors are grateful to the anonymous referee(s) for providing valuable comments and suggestions on the earlier version of this paper which significantly improved the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is partially supported by the Fundamental Research Funds for the Central Universities (grant number 20720220044) and the National Natural Science Foundation of China (Nos. 12171405; 11661074).
{"title":"Valuing equity-linked annuities under high-water mark fee structure","authors":"Kaixin Yan, Shuanming Li, Aili Zhang","doi":"10.1080/03461238.2023.2275276","DOIUrl":"https://doi.org/10.1080/03461238.2023.2275276","url":null,"abstract":"AbstractThis paper studies the valuation of equity-linked investment products embedded with a high-water mark (HWM) fee structure. Under the HWM fee structure, the insurance company charges threshold fees at a constant rate from the policyholder's account whenever the account value is lower than a pre-specified level, and levies HMW fees at another constant rate whenever the account is hitting new record highs that are higher than another pre-specified level. The dynamics of the logarithmic value of the policyholder's account, before fees, is assumed to follow either a two-sided jump-diffusion process with double exponential jumps, or a down-ward jump-diffusion process with exponential jumps. For the two-sided jump-diffusion model with HWM fees, using the Wiener–Hopf factorisation theorem and the duality lemma, we derive an explicit expression for its potential measure. For the down-ward jump-diffusion model with both threshold fees and HWM fees, we are facilitated with the excursion theory to derive an explicit expression of the potential measure. Using the above newly derived potential measures, we are able to obtain formulas for valuing the equity-linked annuity under the HWM fee structure. Finally, we illustrate our results with some numerical examples.KEYWORDS: Equity-linked annuityhigh-water mark fee structurejump-diffusion process AcknowledgementsThe authors are grateful to the anonymous referee(s) for providing valuable comments and suggestions on the earlier version of this paper which significantly improved the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is partially supported by the Fundamental Research Funds for the Central Universities (grant number 20720220044) and the National Natural Science Foundation of China (Nos. 12171405; 11661074).","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352101","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}
Pub Date : 2023-10-31DOI: 10.1080/03461238.2023.2274096
Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song
AbstractIn order to deal with the aging problem, the pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the ‘Samuelson-Aaron’ criterion to age-dependent preference orderings. Under the baseline model, we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort's population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts' weight in the government's decision-making. The optimal mix is the comprehensive result of the two effects.Keywords: Optimal mixPAYGO pensionEET pensionNash equilibriumshrinking population2010 Mathematics Subject Classifications: 91G0591B05JEL CLASSIFICATIONS: G22C61D81 AcknowledgmentsThe authors are particularly grateful to the two anonymous referees and the editor whose suggestions greatly improve the manuscript's quality. The authors also thank the members of the group of Actuarial Sciences and Mathematical Finance at the Department of Mathematical Sciences, Tsinghua University for their feedbacks and useful conversations.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors acknowledge the support from the National Natural Science Foundation of China [grant numbers 12271290, 11871036].
{"title":"Optimal mix among PAYGO, EET and individual savings","authors":"Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song","doi":"10.1080/03461238.2023.2274096","DOIUrl":"https://doi.org/10.1080/03461238.2023.2274096","url":null,"abstract":"AbstractIn order to deal with the aging problem, the pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the ‘Samuelson-Aaron’ criterion to age-dependent preference orderings. Under the baseline model, we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort's population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts' weight in the government's decision-making. The optimal mix is the comprehensive result of the two effects.Keywords: Optimal mixPAYGO pensionEET pensionNash equilibriumshrinking population2010 Mathematics Subject Classifications: 91G0591B05JEL CLASSIFICATIONS: G22C61D81 AcknowledgmentsThe authors are particularly grateful to the two anonymous referees and the editor whose suggestions greatly improve the manuscript's quality. The authors also thank the members of the group of Actuarial Sciences and Mathematical Finance at the Department of Mathematical Sciences, Tsinghua University for their feedbacks and useful conversations.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors acknowledge the support from the National Natural Science Foundation of China [grant numbers 12271290, 11871036].","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135928317","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}
Pub Date : 2023-10-10DOI: 10.1080/03461238.2023.2264555
Zied Chaieb, Domenico De Giovanni, Djibril Gueye
AbstractWe combine two recent credit risk models with the Marshall–Olkin setup to capture the dependence structure of bivariate survival functions. The main advantage of this approach is to handle fatal shock events in the dependence structure since these two credit risk models allow one to match the time of death of an individual with a catastrophe time event. We also provide a methodology for adding other sources of dependency to our approach. In such a setup, we derive the no-arbitrage prices of some common life insurance products for coupled lives. We demonstrate the performance of our method by investigating Sibuya's dependence function. Calibration is done on the data of joint life contracts from a Canadian company.Keywords: Intensity-based modelsdependence structurefatal shock eventsjoint life insurance AcknowledgmentsThis paper has benefited from the valuable comments of one anonymous reviewer, whom the authors wish to thank. The remaining errors are the authors' only responsibility.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Throughout the paper x and y denote the ages of the husband and wife, respectively.2 Here, we have considered the independent case just for simplicity, but we could also consider, in the same spirit, the dependent case for the joint survival function using a copula function.3 In our setup, we have P(τx>s|Ft)=E[e−Γsx|FtW]E[e−Ks|FtK]. Analogous calculations can be done for the marginal probability P(τy>s|Ft).4 The authors wish to thank the Society of Actuaries, through the courtesy of Edward (Jed) Frees and Emiliano A. Valdez, for making available the data in this paper.5 This functional form of the marginal survival probability comes from assuming a stochastic intensity of the form dμh(u)=ahμh(u)+σhμh(h)dWh(u), with a,σ>0. A sufficient condition for Sh(u;t) to be a valid survival function is σ2<2dc. Additional details about this model can be found in Luciano et al. (Citation2008), Luciano & Vigna (Citation2005).6 Luciano et al. (Citation2008) refers to this model of association as the 4.2.20 Nelsen copula function. Originally proposed in Nelsen (Citation2007), a detailed study can be found in Spreeuw (Citation2006). The choice of this particular model of association is because it produces the best fit in a range of several Archimedean copulas for the data used in this paper (Luciano et al. Citation2008).Additional informationFundingDomenico De Giovanni gratefully acknowledges financial support from the PNRR project ‘Italian Ageing, Age-It’ (PE0000015 - CUP H73C22000900006) and Ministry of University and Research of Italy.
摘要本文结合两个最新的信用风险模型，利用Marshall-Olkin设置来捕捉二元生存函数的依赖结构。这种方法的主要优点是在依赖结构中处理致命冲击事件，因为这两种信用风险模型允许将个体的死亡时间与灾难时间事件相匹配。我们还提供了一种将其他依赖源添加到我们的方法中的方法。在这种情况下，我们推导了一些普通人寿保险产品的无套利价格。我们通过研究Sibuya的依赖函数来证明我们的方法的性能。校准是根据加拿大一家公司的联合寿命合同数据完成的。关键词:基于强度的模型;依赖性;结构性冲击事件;共同人寿保险。剩下的错误是作者唯一的责任。披露声明作者未报告潜在的利益冲突。注1在整个论文中，x和y分别表示丈夫和妻子的年龄这里，为了简单起见，我们考虑了独立的情况，但我们也可以考虑，同样的精神，联合生存函数的相关情况，使用一个联结函数在我们的设置中，我们有P(τx>s|Ft)=E[E−Γsx|FtW]E[E−Ks|FtK]。边际概率P(τy>s |ft)也可以进行类似的计算作者希望感谢精算师协会，感谢Edward (Jed) Frees和Emiliano A. Valdez提供本文中的数据这种边际生存概率的函数形式来自于假设随机强度为dμh(u)=ahμh(u)+σhμh(h)dWh(u)，其中a为σ>0。Sh(u;t)是有效生存函数的充分条件是σ2<2dc。关于该模型的更多细节可以在Luciano et al. (Citation2008)， Luciano & Vigna (Citation2005)中找到Luciano et al. (Citation2008)将这种关联模型称为4.2.20 nelson copula函数。最初由Nelsen (Citation2007)提出，详细的研究可以在Spreeuw (Citation2006)中找到。选择这种特殊的关联模型是因为它对本文使用的数据产生了几个阿基米德copula的最佳拟合(Luciano等)。Citation2008)。domenico De Giovanni感谢PNRR项目“意大利老龄化，Age-It”(PE0000015 - CUP H73C22000900006)和意大利大学和研究部的资金支持。
{"title":"Two hybrid models for dependent death times of couple: a common shock approach","authors":"Zied Chaieb, Domenico De Giovanni, Djibril Gueye","doi":"10.1080/03461238.2023.2264555","DOIUrl":"https://doi.org/10.1080/03461238.2023.2264555","url":null,"abstract":"AbstractWe combine two recent credit risk models with the Marshall–Olkin setup to capture the dependence structure of bivariate survival functions. The main advantage of this approach is to handle fatal shock events in the dependence structure since these two credit risk models allow one to match the time of death of an individual with a catastrophe time event. We also provide a methodology for adding other sources of dependency to our approach. In such a setup, we derive the no-arbitrage prices of some common life insurance products for coupled lives. We demonstrate the performance of our method by investigating Sibuya's dependence function. Calibration is done on the data of joint life contracts from a Canadian company.Keywords: Intensity-based modelsdependence structurefatal shock eventsjoint life insurance AcknowledgmentsThis paper has benefited from the valuable comments of one anonymous reviewer, whom the authors wish to thank. The remaining errors are the authors' only responsibility.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Throughout the paper x and y denote the ages of the husband and wife, respectively.2 Here, we have considered the independent case just for simplicity, but we could also consider, in the same spirit, the dependent case for the joint survival function using a copula function.3 In our setup, we have P(τx>s|Ft)=E[e−Γsx|FtW]E[e−Ks|FtK]. Analogous calculations can be done for the marginal probability P(τy>s|Ft).4 The authors wish to thank the Society of Actuaries, through the courtesy of Edward (Jed) Frees and Emiliano A. Valdez, for making available the data in this paper.5 This functional form of the marginal survival probability comes from assuming a stochastic intensity of the form dμh(u)=ahμh(u)+σhμh(h)dWh(u), with a,σ>0. A sufficient condition for Sh(u;t) to be a valid survival function is σ2<2dc. Additional details about this model can be found in Luciano et al. (Citation2008), Luciano & Vigna (Citation2005).6 Luciano et al. (Citation2008) refers to this model of association as the 4.2.20 Nelsen copula function. Originally proposed in Nelsen (Citation2007), a detailed study can be found in Spreeuw (Citation2006). The choice of this particular model of association is because it produces the best fit in a range of several Archimedean copulas for the data used in this paper (Luciano et al. Citation2008).Additional informationFundingDomenico De Giovanni gratefully acknowledges financial support from the PNRR project ‘Italian Ageing, Age-It’ (PE0000015 - CUP H73C22000900006) and Ministry of University and Research of Italy.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294864","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}
Pub Date : 2023-10-06DOI: 10.1080/03461238.2023.2257405
Benjamin Avanzi, Hayden Lau, Mogens Steffensen
We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the P and Q measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.
{"title":"Optimal reinsurance design under solvency constraints","authors":"Benjamin Avanzi, Hayden Lau, Mogens Steffensen","doi":"10.1080/03461238.2023.2257405","DOIUrl":"https://doi.org/10.1080/03461238.2023.2257405","url":null,"abstract":"We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the P and Q measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350645","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}
Pub Date : 2023-09-18DOI: 10.1080/03461238.2023.2258135
Julie Huyghe, Julien Trufin, Michel Denuit
AbstractThis paper proposes a new boosting machine based on forward stagewise additive modeling with cost-complexity pruned trees. In the Tweedie case, it deals directly with observed responses, not gradients of the loss function. Trees included in the score progressively reduce to the root-node one, in an adaptive way. The proposed Adaptive Boosting Tree (ABT) machine thus automatically stops at that time, avoiding to resort to the time-consuming cross validation approach. Case studies performed on motor third-party liability insurance claim data demonstrate the performances of the proposed ABT machine for ratemaking, in comparison with regular gradient boosting trees.Keywords: Risk classificationboostinggradient boostingregression treescost-complexity pruning Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Boosting cost-complexity pruned trees on Tweedie responses: the ABT machine for insurance ratemaking","authors":"Julie Huyghe, Julien Trufin, Michel Denuit","doi":"10.1080/03461238.2023.2258135","DOIUrl":"https://doi.org/10.1080/03461238.2023.2258135","url":null,"abstract":"AbstractThis paper proposes a new boosting machine based on forward stagewise additive modeling with cost-complexity pruned trees. In the Tweedie case, it deals directly with observed responses, not gradients of the loss function. Trees included in the score progressively reduce to the root-node one, in an adaptive way. The proposed Adaptive Boosting Tree (ABT) machine thus automatically stops at that time, avoiding to resort to the time-consuming cross validation approach. Case studies performed on motor third-party liability insurance claim data demonstrate the performances of the proposed ABT machine for ratemaking, in comparison with regular gradient boosting trees.Keywords: Risk classificationboostinggradient boostingregression treescost-complexity pruning Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135149922","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}
Pub Date : 2023-09-13DOI: 10.1080/03461238.2023.2256508
Yang Yang, Yahui Fan, Kam Chuen Yuen
AbstractThis paper is devoted to asymptotic analysis for a continuous-time risk model with the insurance surplus process and the log-price process of the investment driven by two dependent jump-diffusion processes. We take into account arbitrary dependence between the insurance claims and their corresponding investment return jumps caused by a sequence of systematic factors, whose arrival times constitute a renewal counting process. Under the framework of regular variation, we obtain a simple and unified asymptotic formula for the finite-time ruin probability as the initial wealth becomes large. It turns out that, in the weakly dependent case, the tails of the claims determine the exact decay rate of the finite-time ruin probability while the investment return jumps only contribute to the coefficient of the asymptotic formula; however, in the strongly dependent case, they both produce essential impacts on the finite-time ruin probability which is under-estimated in the weakly dependent case.Keywords: Asymptoticsfinite-time ruin probabilitysystematic factorsinsurance claimsinvestment return jumpsMSC: 62P0562E1091B30 AcknowledgmentsThe authors would like to thank the anonymous referee for his/her suggestive comments and very careful reading of the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 According to the American Council of Life Insurers, ‘life insurers are a major source of bond financing for American business, holding more than 22% of all U.S. corporate bonds’ and ‘life insurers provide long-term capital to the commercial mortgage market, financing more than 515 billion dollars, or almost one-sixth, of U.S. commercial mortgages’. The Annual Report 2021 of Allianz Group stated that as of 31 December 2021, the overall asset portfolio has reached 808.5 billion euros mainly in the debt investments (672.3 billion decreased by 10.1 billion compared to year end 2020, mainly due to market movements), about 91% of which was invested in investment-grade bonds and loans. See page 90. Available at https://www.allianz.com/en/investorrelations/results-reports/annual-reports.2 See a report from the International Monetary Fund (2016). The insurance sector: trends and systemic risks implications. Available at https://www.imf.org/External/Pubs/FT/GFSR/2016/01/pdf/c3.pdf.3 The collapse and near-failure of the insurance giant American International Group was caused largely by its 526 billion dollars portfolio of credit default swaps.4 The American Property Casualty Insurance Association estimated that the monthly COVID-19 business interruption losses just for businesses with 100 or fewer employees was 255–431 billion dollars per month. Available at http://www.pciaa.net/pciwebsite/cms/content/viewpage?sitePageId=60052.5 The business segment Asset Management of the Allianz Group was impacted by the severe financial market disruption and related investor uncertainties which led to a negative market valuation of as
摘要本文研究了一类具有保险盈余过程和投资对数价格过程的连续时间风险模型的渐近分析，该模型由两个依赖的跳跃扩散过程驱动。我们考虑了由一系列系统因素引起的保险索赔与其相应的投资回报跳跃之间的任意依赖关系，这些因素的到达时间构成了续期计数过程。在正则变分的框架下，得到了初始财富变大时有限时间破产概率的一个简单统一的渐近公式。结果表明，在弱相关情况下，债权的尾部决定了有限时间破产概率的确切衰减率，而投资收益的跳跃只对渐近公式的系数有贡献;然而，在强依赖情况下，它们都对有限时间破产概率产生重要影响，而在弱依赖情况下，有限时间破产概率被低估。关键词:渐近有限时间破产概率系统因素保险理赔投资回报跳跃感谢匿名审稿人的提意见和对本文的认真阅读。披露声明作者未报告潜在的利益冲突。注1根据美国人寿保险委员会的数据，“人寿保险公司是美国企业债券融资的主要来源，持有超过22%的美国公司债券”，“人寿保险公司为商业抵押贷款市场提供长期资本，融资超过5150亿美元，几乎占美国商业抵押贷款的六分之一”。安联集团2021年年度报告指出，截至2021年12月31日，整体资产组合已达到8085亿欧元，主要是债务投资(与2020年底相比，6723亿欧元减少了101亿欧元，主要是由于市场波动)，其中约91%投资于投资级债券和贷款。见第90页。参见国际货币基金组织(2016)的一份报告。保险业:趋势和系统性风险影响。3.可从https://www.imf.org/External/Pubs/FT/GFSR/2016/01/pdf/c3.pdf.3找到保险业巨头美国国际集团的崩溃和濒临破产，主要是由其5260亿美元的信用违约掉期投资组合造成的美国财产损失保险协会估计，每月因新冠肺炎疫情，员工人数在100人以下的企业的业务中断损失为2550亿美元至4310亿美元。安联集团的资产管理业务部门受到严重的金融市场混乱和相关投资者不确定性的影响，导致管理下资产的市场估值为负，并在2020年第一季度出现净流出。然而，在随后的几个季度中，该业务部门通过达到强劲的积极市场效应和第三方净流入而完全恢复。同时，截至2020年12月31日，财产-意外险业务部门受到了11亿英镑的负面影响。损失由意外的业务中断、娱乐和信贷造成。参见《安联集团2020年年报》122页。澳大利亚保险委员会(Insurance Council of Australia)估计，与气候有关的极端事件每年造成的保险损失总额为37亿美元，其中严重的森林大火占22亿美元。http://www.icadataglobe.com/access-catastrophe-data/(2020年6月访问)私人保险业管理着超过16万亿美元的资金，其全球资产也将面临未来气候风险。气候变化的实际影响将直接影响保险和再保险公司的投资部门。应该认识到，对保险公司投资组合的风险评估需要纳入对气候变化影响的分析。参见Herweijer et al. (Citation2009)和gizio et al. (Citation2019)。杨洋感谢国家社科基金(No. 22BTJ060)、教育部人文社会科学基金(No. 20YJA910006)、江苏省自然科学基金(No. 20YJA910006)的资助。BK20201396)，江苏省高校自然科学基金项目(23KJA110002)。范亚辉感谢江苏省教育厅研究生科研与实践创新项目(项目编号:1139902)的资助。KYCX23_2268)。 锦泉园感谢中国香港特别行政区研究资助局(研究资助局编号:HKU17306220)。
{"title":"Ruin in a continuous-time risk model with arbitrarily dependent insurance and financial risks triggered by systematic factors","authors":"Yang Yang, Yahui Fan, Kam Chuen Yuen","doi":"10.1080/03461238.2023.2256508","DOIUrl":"https://doi.org/10.1080/03461238.2023.2256508","url":null,"abstract":"AbstractThis paper is devoted to asymptotic analysis for a continuous-time risk model with the insurance surplus process and the log-price process of the investment driven by two dependent jump-diffusion processes. We take into account arbitrary dependence between the insurance claims and their corresponding investment return jumps caused by a sequence of systematic factors, whose arrival times constitute a renewal counting process. Under the framework of regular variation, we obtain a simple and unified asymptotic formula for the finite-time ruin probability as the initial wealth becomes large. It turns out that, in the weakly dependent case, the tails of the claims determine the exact decay rate of the finite-time ruin probability while the investment return jumps only contribute to the coefficient of the asymptotic formula; however, in the strongly dependent case, they both produce essential impacts on the finite-time ruin probability which is under-estimated in the weakly dependent case.Keywords: Asymptoticsfinite-time ruin probabilitysystematic factorsinsurance claimsinvestment return jumpsMSC: 62P0562E1091B30 AcknowledgmentsThe authors would like to thank the anonymous referee for his/her suggestive comments and very careful reading of the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 According to the American Council of Life Insurers, ‘life insurers are a major source of bond financing for American business, holding more than 22% of all U.S. corporate bonds’ and ‘life insurers provide long-term capital to the commercial mortgage market, financing more than 515 billion dollars, or almost one-sixth, of U.S. commercial mortgages’. The Annual Report 2021 of Allianz Group stated that as of 31 December 2021, the overall asset portfolio has reached 808.5 billion euros mainly in the debt investments (672.3 billion decreased by 10.1 billion compared to year end 2020, mainly due to market movements), about 91% of which was invested in investment-grade bonds and loans. See page 90. Available at https://www.allianz.com/en/investorrelations/results-reports/annual-reports.2 See a report from the International Monetary Fund (2016). The insurance sector: trends and systemic risks implications. Available at https://www.imf.org/External/Pubs/FT/GFSR/2016/01/pdf/c3.pdf.3 The collapse and near-failure of the insurance giant American International Group was caused largely by its 526 billion dollars portfolio of credit default swaps.4 The American Property Casualty Insurance Association estimated that the monthly COVID-19 business interruption losses just for businesses with 100 or fewer employees was 255–431 billion dollars per month. Available at http://www.pciaa.net/pciwebsite/cms/content/viewpage?sitePageId=60052.5 The business segment Asset Management of the Allianz Group was impacted by the severe financial market disruption and related investor uncertainties which led to a negative market valuation of as","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784501","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}
Pub Date : 2023-09-12DOI: 10.1080/03461238.2023.2251197
Kira Henshaw, Michel Mandjes, Corina Constantinescu
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