Pub Date : 2022-07-31DOI: 10.1080/03461238.2022.2104131
P. Lyu, J. S. Li, K. Zhou
In this paper, we address the mortality modeling needs for pension plan sponsors who wish to use index-based solutions to mitigate their longevity risk exposures. Specifically, we propose the three-way Li-Lee (TWLL) model, which enforces a certain extent of coherence between the population to which the index-based hedging instrument is linked and the population of pension plan members, and at the same time incorporates the empirical fact that mortality improvement rates of different socioeconomic subgroups in the pension plan are persistently different. We further develop a delta longevity hedging strategy that is compatible with the TWLL model. With the aid of real mortality data, we demonstrate that if persistent socioeconomic differentials in mortality improvement rates exist but are not considered in an index-based longevity hedge, the performance of the hedge could be compromised, and the extent of underperformance would depend on the distributions of pension plan members and pension amounts across different socioeconomic subgroups. This problem can be alleviated if the longevity hedge is calibrated on the basis of the TWLL model.
{"title":"Socioeconomic differentials in mortality: implications on index-based longevity hedges","authors":"P. Lyu, J. S. Li, K. Zhou","doi":"10.1080/03461238.2022.2104131","DOIUrl":"https://doi.org/10.1080/03461238.2022.2104131","url":null,"abstract":"In this paper, we address the mortality modeling needs for pension plan sponsors who wish to use index-based solutions to mitigate their longevity risk exposures. Specifically, we propose the three-way Li-Lee (TWLL) model, which enforces a certain extent of coherence between the population to which the index-based hedging instrument is linked and the population of pension plan members, and at the same time incorporates the empirical fact that mortality improvement rates of different socioeconomic subgroups in the pension plan are persistently different. We further develop a delta longevity hedging strategy that is compatible with the TWLL model. With the aid of real mortality data, we demonstrate that if persistent socioeconomic differentials in mortality improvement rates exist but are not considered in an index-based longevity hedge, the performance of the hedge could be compromised, and the extent of underperformance would depend on the distributions of pension plan members and pension amounts across different socioeconomic subgroups. This problem can be alleviated if the longevity hedge is calibrated on the basis of the TWLL model.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73903475","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 : 2022-07-18DOI: 10.1080/03461238.2022.2092891
Sophie de Mol van Otterloo, Jennifer Alonso-García
We investigate the effect of part-time and full-time work on health using a Markov framework and generalized linear models to smooth the resulting crude rates. The Chapman-Kolmogorov equations are used for a general solution. We apply this model to assess a partial early retirement incentive in the Netherlands, known as ‘the generation pact’. The smoothed rates imply that working part time does not necessarily mean a better health for the elderly. In fact, men are healthier when working full time, while women fall sick more often when working full time but recover more often as well. However, when comparing the future rates of a person currently aged 50 working full time and using the generation pact, both the recovery and the morbidity rates drop when starting the generation pact. A stylized assessment of the costs associated yields that costs drop by half when using the generation pact.
{"title":"A multi-state model for sick leave and its impact on partial early retirement incentives: the case of the Netherlands","authors":"Sophie de Mol van Otterloo, Jennifer Alonso-García","doi":"10.1080/03461238.2022.2092891","DOIUrl":"https://doi.org/10.1080/03461238.2022.2092891","url":null,"abstract":"We investigate the effect of part-time and full-time work on health using a Markov framework and generalized linear models to smooth the resulting crude rates. The Chapman-Kolmogorov equations are used for a general solution. We apply this model to assess a partial early retirement incentive in the Netherlands, known as ‘the generation pact’. The smoothed rates imply that working part time does not necessarily mean a better health for the elderly. In fact, men are healthier when working full time, while women fall sick more often when working full time but recover more often as well. However, when comparing the future rates of a person currently aged 50 working full time and using the generation pact, both the recovery and the morbidity rates drop when starting the generation pact. A stylized assessment of the costs associated yields that costs drop by half when using the generation pact.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83698841","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 : 2022-07-12DOI: 10.1080/03461238.2022.2089051
Eric C. K. Cheung, Hayden Lau, G. Willmot, J. Woo
In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk model. Traditional general solutions to finite-time ruin problems are usually expressed in terms of infinite sums involving the convolutions related to the claim size distribution and their integrals, which can typically be evaluated only in special cases where the claims follow exponential or (more generally) mixed Erlang distribution. We propose to tackle the partial integro-differential equation satisfied by the finite-time ruin probability and develop a new approach to obtain a solution in terms of bivariate Laguerre series as a function of the initial surplus level and the time horizon for a large class of light-tailed claim distributions. To illustrate the versatility and accuracy of our proposed method which is easy to implement, numerical examples are provided for claim amount distributions such as generalized inverse Gaussian, Weibull and truncated normal where closed-form convolutions are not available in the literature.
{"title":"Finite-time ruin probabilities using bivariate Laguerre series","authors":"Eric C. K. Cheung, Hayden Lau, G. Willmot, J. Woo","doi":"10.1080/03461238.2022.2089051","DOIUrl":"https://doi.org/10.1080/03461238.2022.2089051","url":null,"abstract":"In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk model. Traditional general solutions to finite-time ruin problems are usually expressed in terms of infinite sums involving the convolutions related to the claim size distribution and their integrals, which can typically be evaluated only in special cases where the claims follow exponential or (more generally) mixed Erlang distribution. We propose to tackle the partial integro-differential equation satisfied by the finite-time ruin probability and develop a new approach to obtain a solution in terms of bivariate Laguerre series as a function of the initial surplus level and the time horizon for a large class of light-tailed claim distributions. To illustrate the versatility and accuracy of our proposed method which is easy to implement, numerical examples are provided for claim amount distributions such as generalized inverse Gaussian, Weibull and truncated normal where closed-form convolutions are not available in the literature.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84234544","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 : 2022-07-08DOI: 10.1080/03461238.2022.2094718
Yuanying Guan, A. Tsanakas, Ruodu Wang
Two natural and potentially useful properties for capital allocation rules are top-down consistency and shrinking independence. Top-down consistency means that the total capital is determined by the aggregate portfolio risk. Shrinking independence means that the risk capital allocated to a given business line should not be affected by a proportional reduction of exposure in another business line. These two properties are satisfied by, respectively, the Euler allocation rule and the stress allocation rule. We prove an impossibility theorem that states that these two properties jointly lead to the trivial capital allocation based on the mean. When a subadditive risk measure is used, the same result holds for weaker versions of shrinking independence, which prevents the increase in risk capital in one line, when exposure to another is reduced. The impossibility theorem remains valid even if one assumes strong positive dependence among the risk vectors.
{"title":"An impossibility theorem on capital allocation","authors":"Yuanying Guan, A. Tsanakas, Ruodu Wang","doi":"10.1080/03461238.2022.2094718","DOIUrl":"https://doi.org/10.1080/03461238.2022.2094718","url":null,"abstract":"Two natural and potentially useful properties for capital allocation rules are top-down consistency and shrinking independence. Top-down consistency means that the total capital is determined by the aggregate portfolio risk. Shrinking independence means that the risk capital allocated to a given business line should not be affected by a proportional reduction of exposure in another business line. These two properties are satisfied by, respectively, the Euler allocation rule and the stress allocation rule. We prove an impossibility theorem that states that these two properties jointly lead to the trivial capital allocation based on the mean. When a subadditive risk measure is used, the same result holds for weaker versions of shrinking independence, which prevents the increase in risk capital in one line, when exposure to another is reduced. The impossibility theorem remains valid even if one assumes strong positive dependence among the risk vectors.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81681370","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 : 2022-07-04DOI: 10.1080/03461238.2022.2147862
H. Albrecher, Brandon Garcia Flores
We reconsider the study of optimal dividend strategies in the Cramér-Lundberg risk model. It is well-known that the solution of the classical dividend problem is in general a band strategy. However, the numerical techniques for the identification of the optimal bands available in the literature are very hard to implement and explicit numerical results are known for very few cases only. In this paper we put a gradient-based method into place which allows to determine optimal bands in more general situations. In addition, we adapt an evolutionary algorithm to this dividend problem, which is not as fast, but applicable in considerable generality, and can serve for providing a competitive benchmark. We illustrate the proposed methods in concrete examples, reproducing earlier results in the literature as well as establishing new ones for claim size distributions that could not be studied before.
{"title":"Optimal dividend bands revisited: a gradient-based method and evolutionary algorithms","authors":"H. Albrecher, Brandon Garcia Flores","doi":"10.1080/03461238.2022.2147862","DOIUrl":"https://doi.org/10.1080/03461238.2022.2147862","url":null,"abstract":"We reconsider the study of optimal dividend strategies in the Cramér-Lundberg risk model. It is well-known that the solution of the classical dividend problem is in general a band strategy. However, the numerical techniques for the identification of the optimal bands available in the literature are very hard to implement and explicit numerical results are known for very few cases only. In this paper we put a gradient-based method into place which allows to determine optimal bands in more general situations. In addition, we adapt an evolutionary algorithm to this dividend problem, which is not as fast, but applicable in considerable generality, and can serve for providing a competitive benchmark. We illustrate the proposed methods in concrete examples, reproducing earlier results in the literature as well as establishing new ones for claim size distributions that could not be studied before.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79878591","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 : 2022-06-30DOI: 10.1080/03461238.2022.2161413
Bavo D. C. Campo, Katrien Antonio
Actuaries use predictive modeling techniques to assess the loss cost on a contract as a function of observable risk characteristics. State-of-the-art statistical and machine learning methods are not well equipped to handle hierarchically structured risk factors with a large number of levels. In this paper, we demonstrate the data-driven construction of an insurance pricing model when hierarchically structured risk factors, contract-specific as well as externally collected risk factors are available. We examine the pricing of a workers' compensation insurance product with a hierarchical credibility model [Jewell, W. S. (1975). The use of collateral data in credibility theory: A hierarchical model. Laxenburg: IIASA], Ohlsson's combination of a generalized linear and a hierarchical credibility model [Ohlsson, E. (2008). Combining generalized linear models and credibility models in practice. Scandinavian Actuarial Journal 2008(4), 301–314] and mixed models. We compare the predictive performance of these models and evaluate the effect of the distributional assumption on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models. For our case-study the Tweedie distribution is well suited to model and predict the loss cost on a contract. Moreover, incorporating contract-specific risk factors in the model improves the predictive performance and the risk differentiation in our workers' compensation insurance portfolio.
{"title":"Insurance pricing with hierarchically structured data an illustration with a workers' compensation insurance portfolio","authors":"Bavo D. C. Campo, Katrien Antonio","doi":"10.1080/03461238.2022.2161413","DOIUrl":"https://doi.org/10.1080/03461238.2022.2161413","url":null,"abstract":"Actuaries use predictive modeling techniques to assess the loss cost on a contract as a function of observable risk characteristics. State-of-the-art statistical and machine learning methods are not well equipped to handle hierarchically structured risk factors with a large number of levels. In this paper, we demonstrate the data-driven construction of an insurance pricing model when hierarchically structured risk factors, contract-specific as well as externally collected risk factors are available. We examine the pricing of a workers' compensation insurance product with a hierarchical credibility model [Jewell, W. S. (1975). The use of collateral data in credibility theory: A hierarchical model. Laxenburg: IIASA], Ohlsson's combination of a generalized linear and a hierarchical credibility model [Ohlsson, E. (2008). Combining generalized linear models and credibility models in practice. Scandinavian Actuarial Journal 2008(4), 301–314] and mixed models. We compare the predictive performance of these models and evaluate the effect of the distributional assumption on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models. For our case-study the Tweedie distribution is well suited to model and predict the loss cost on a contract. Moreover, incorporating contract-specific risk factors in the model improves the predictive performance and the risk differentiation in our workers' compensation insurance portfolio.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87614655","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 : 2022-06-30DOI: 10.1080/03461238.2022.2092419
Hamza Hanbali, Daniël Linders, Jan Dhaene
ABSTRACT The Value-at-Risk (VaR) of comonotonic sums can be decomposed into marginal VaRs at the same level. This additivity property allows to derive useful decompositions for other risk measures. In particular, the Tail Value-at-Risk (TVaR) and the upper tail transform of comonotonic sums can be written as the sum of their corresponding marginal risk measures. The other extreme dependence situation, involving the sum of two arbitrary counter-monotonic random variables, presents a certain number of challenges. One of them is that it is not straightforward to express the VaR of a counter-monotonic sum in terms of the VaRs of the marginal components of the sum. This paper generalizes the results derived in [Chaoubi, I., Cossette, H., Gadoury, S.-P. & Marceau, E. (2020). On sums of two counter-monotonic risks. Insurance: Mathematics and Economics 92, 47–60.] by providing decomposition formulas for the VaR, TVaR and the stop-loss transform of the sum of two arbitrary counter-monotonic random variables.
共单调和的风险值(VaR)可以分解为相同水平上的边际VaR。这种可加性允许为其他风险度量导出有用的分解。其中，共单调和的尾部风险值(TVaR)和上尾变换可以写成它们对应的边际风险测度的和。另一种极端依赖情况，涉及两个任意反单调随机变量的和，提出了一些挑战。其中之一是用和的边缘分量的VaR来表示反单调和的VaR是不直接的。本文推广了[Chaoubi, I.， Cossette, H.， Gadoury, s . p .]&马尔索，E.(2020)。关于两个反单调风险的和。保险:数学与经济92,47-60。]通过提供VaR、TVaR和两个任意反单调随机变量和的止损变换的分解公式。
{"title":"Value-at-Risk, Tail Value-at-Risk and upper tail transform of the sum of two counter-monotonic random variables","authors":"Hamza Hanbali, Daniël Linders, Jan Dhaene","doi":"10.1080/03461238.2022.2092419","DOIUrl":"https://doi.org/10.1080/03461238.2022.2092419","url":null,"abstract":"ABSTRACT The Value-at-Risk (VaR) of comonotonic sums can be decomposed into marginal VaRs at the same level. This additivity property allows to derive useful decompositions for other risk measures. In particular, the Tail Value-at-Risk (TVaR) and the upper tail transform of comonotonic sums can be written as the sum of their corresponding marginal risk measures. The other extreme dependence situation, involving the sum of two arbitrary counter-monotonic random variables, presents a certain number of challenges. One of them is that it is not straightforward to express the VaR of a counter-monotonic sum in terms of the VaRs of the marginal components of the sum. This paper generalizes the results derived in [Chaoubi, I., Cossette, H., Gadoury, S.-P. & Marceau, E. (2020). On sums of two counter-monotonic risks. Insurance: Mathematics and Economics 92, 47–60.] by providing decomposition formulas for the VaR, TVaR and the stop-loss transform of the sum of two arbitrary counter-monotonic random variables.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87176634","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 : 2022-06-27DOI: 10.1080/03461238.2023.2197442
Martin Bladt, Christian Furrer
The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the product-limit estimator in two different ways with distinct interpretations. Strong uniform consistency is proved for both cases under certain assumptions on the kind of contamination and the quality of expert information, which sheds light on the techniques and decisions that practitioners may take. The nuances of the techniques are discussed -- also with a view towards semi-parametric estimation -- and they are illustrated using simulated and real-world insurance data.
{"title":"Expert Kaplan–Meier estimation","authors":"Martin Bladt, Christian Furrer","doi":"10.1080/03461238.2023.2197442","DOIUrl":"https://doi.org/10.1080/03461238.2023.2197442","url":null,"abstract":"The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the product-limit estimator in two different ways with distinct interpretations. Strong uniform consistency is proved for both cases under certain assumptions on the kind of contamination and the quality of expert information, which sheds light on the techniques and decisions that practitioners may take. The nuances of the techniques are discussed -- also with a view towards semi-parametric estimation -- and they are illustrated using simulated and real-world insurance data.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88083467","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 : 2022-06-08DOI: 10.1080/03461238.2022.2142156
Katia Colaneri, J. Eisenberg, Benedetta Salterini
In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. We set the initial capital to zero in order to verify whether the premia are sufficient to buy reinsurance and to manage the risk of incoming claims in such a way that the desired risk characteristics are achieved at some terminal time without external help (represented, for instance, by a positive initial capital). We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level α. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time.
{"title":"Some optimisation problems in insurance with a terminal distribution constraint","authors":"Katia Colaneri, J. Eisenberg, Benedetta Salterini","doi":"10.1080/03461238.2022.2142156","DOIUrl":"https://doi.org/10.1080/03461238.2022.2142156","url":null,"abstract":"In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. We set the initial capital to zero in order to verify whether the premia are sufficient to buy reinsurance and to manage the risk of incoming claims in such a way that the desired risk characteristics are achieved at some terminal time without external help (represented, for instance, by a positive initial capital). We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level α. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91039683","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 : 2022-06-01DOI: 10.1080/03461238.2022.2139632
Jingyi Cao, Dongchen Li, V. Young, B. Zou
ABSTRACT We consider the problem of to which extent a diffusion process serves as a valid approximation of the classical Cramér-Lundberg (CL) risk process for a Stackelberg differential game between a buyer and a seller of insurance. We show that the equilibrium for the diffusion approximation equals the limit of the equilibrium for the scaled CL process, and it is nearly optimal for the pre-limit problem. Specifically, if the loss process follows a CL risk process and ambiguity is measured via entropic divergence, then the Stackelberg equilibrium of the diffusion approximation with squared-error divergence approximates the equilibrium for the former model to order , in which we scale the CL model via n, as in Cohen and Young [(2020). Rate of convergence of the probability of ruin in the Cramér-Lundberg model to its diffusion approximation. Insurance: Mathematics and Economics 93: 333–340].
{"title":"Asymptotic analysis of a Stackelberg differential game for insurance under model ambiguity","authors":"Jingyi Cao, Dongchen Li, V. Young, B. Zou","doi":"10.1080/03461238.2022.2139632","DOIUrl":"https://doi.org/10.1080/03461238.2022.2139632","url":null,"abstract":"ABSTRACT We consider the problem of to which extent a diffusion process serves as a valid approximation of the classical Cramér-Lundberg (CL) risk process for a Stackelberg differential game between a buyer and a seller of insurance. We show that the equilibrium for the diffusion approximation equals the limit of the equilibrium for the scaled CL process, and it is nearly optimal for the pre-limit problem. Specifically, if the loss process follows a CL risk process and ambiguity is measured via entropic divergence, then the Stackelberg equilibrium of the diffusion approximation with squared-error divergence approximates the equilibrium for the former model to order , in which we scale the CL model via n, as in Cohen and Young [(2020). Rate of convergence of the probability of ruin in the Cramér-Lundberg model to its diffusion approximation. Insurance: Mathematics and Economics 93: 333–340].","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83696778","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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