Pub Date : 2022-02-03DOI: 10.1017/S174849952200001X
Jia Liu, Jackie Li, K. Daly
Abstract Potentialdata breach losses represent a significant part of operational risk and can be a serious concern for risk managers and insurers. In this paper, we employ the vine copulas under a Bayesian framework to co-model incidences from different data breach types. A full Bayesian approach can allow one to select both the copulas and margins and estimate their parameters in a coherent fashion. In particular, it can incorporate process, parameter, and model uncertainties, and this is very important for applications in risk management under current regulations. We also conduct a series of sensitivity tests on the Bayesian modelling results. Using two public data sets of data breach losses, we find that the overall dependency structure and tail dependence vary significantly between different types of data breaches. The optimally selected vine structure and pairwise copulas suggest more conservative value-at-risk estimates when compared to the other suboptimal copula models.
{"title":"Bayesian vine copulas for modelling dependence in data breach losses","authors":"Jia Liu, Jackie Li, K. Daly","doi":"10.1017/S174849952200001X","DOIUrl":"https://doi.org/10.1017/S174849952200001X","url":null,"abstract":"Abstract Potentialdata breach losses represent a significant part of operational risk and can be a serious concern for risk managers and insurers. In this paper, we employ the vine copulas under a Bayesian framework to co-model incidences from different data breach types. A full Bayesian approach can allow one to select both the copulas and margins and estimate their parameters in a coherent fashion. In particular, it can incorporate process, parameter, and model uncertainties, and this is very important for applications in risk management under current regulations. We also conduct a series of sensitivity tests on the Bayesian modelling results. Using two public data sets of data breach losses, we find that the overall dependency structure and tail dependence vary significantly between different types of data breaches. The optimally selected vine structure and pairwise copulas suggest more conservative value-at-risk estimates when compared to the other suboptimal copula models.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"401 - 424"},"PeriodicalIF":1.7,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43657957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-25DOI: 10.1017/S1748499521000269
A. Melnikov, Hongxi Wan
Abstract The main aim of this paper is to develop an optimal partial hedging strategy that minimises an investor’s shortfall subject to an initial wealth constraint. The risk criterion we employ is a robust tail risk measure called Range Value-at-Risk (RVaR) which belongs to a wider class of distortion risk measures and contains the well-known measures VaR and CVaR as important limiting cases. Explicit forms of such RVaR-based optimal hedging strategies are derived. In addition, we provide a numerical example to demonstrate how to apply this more comprehensive methodology of partial hedging in the area of mixed finance/insurance contracts in the market with long-range dependence.
{"title":"On RVaR-based optimal partial hedging","authors":"A. Melnikov, Hongxi Wan","doi":"10.1017/S1748499521000269","DOIUrl":"https://doi.org/10.1017/S1748499521000269","url":null,"abstract":"Abstract The main aim of this paper is to develop an optimal partial hedging strategy that minimises an investor’s shortfall subject to an initial wealth constraint. The risk criterion we employ is a robust tail risk measure called Range Value-at-Risk (RVaR) which belongs to a wider class of distortion risk measures and contains the well-known measures VaR and CVaR as important limiting cases. Explicit forms of such RVaR-based optimal hedging strategies are derived. In addition, we provide a numerical example to demonstrate how to apply this more comprehensive methodology of partial hedging in the area of mixed finance/insurance contracts in the market with long-range dependence.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"349 - 366"},"PeriodicalIF":1.7,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43006127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-19DOI: 10.1017/S1748499521000245
T. Maynard, Luca Baldassarre, Y. de Montjoye, L. McFall, M. Óskarsdóttir
Abstract AI has had many summers and winters. Proponents have overpromised, and there has been hype and disappointment. In recent years, however, we have watched with awe, surprise, and hope at the successes: Better than human capabilities of image-recognition; winning at Go; useful chatbots that seem to understand your needs; recommendation algorithms harvesting the wisdom of crowds. And with this success comes the spectre of danger. Machine behaviours that embed the worst of human prejudice and biases; techniques trying to exploit human weaknesses to skew elections or prompt self-harming behaviours. Are we seeing a perfect storm of social media, sensor technologies, new algorithms and edge computing? With this backdrop: is AI coming of age?
{"title":"AI: Coming of age?","authors":"T. Maynard, Luca Baldassarre, Y. de Montjoye, L. McFall, M. Óskarsdóttir","doi":"10.1017/S1748499521000245","DOIUrl":"https://doi.org/10.1017/S1748499521000245","url":null,"abstract":"Abstract AI has had many summers and winters. Proponents have overpromised, and there has been hype and disappointment. In recent years, however, we have watched with awe, surprise, and hope at the successes: Better than human capabilities of image-recognition; winning at Go; useful chatbots that seem to understand your needs; recommendation algorithms harvesting the wisdom of crowds. And with this success comes the spectre of danger. Machine behaviours that embed the worst of human prejudice and biases; techniques trying to exploit human weaknesses to skew elections or prompt self-harming behaviours. Are we seeing a perfect storm of social media, sensor technologies, new algorithms and edge computing? With this backdrop: is AI coming of age?","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"1 - 5"},"PeriodicalIF":1.7,"publicationDate":"2022-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46584743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-24DOI: 10.1017/s1748499523000064
G. Taylor, Phuong Vu
The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses “auto-balanced” models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.
{"title":"Auto-balanced common shock claim models","authors":"G. Taylor, Phuong Vu","doi":"10.1017/s1748499523000064","DOIUrl":"https://doi.org/10.1017/s1748499523000064","url":null,"abstract":"\u0000 The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses “auto-balanced” models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45618622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-19DOI: 10.1017/s1748499521000221
Hamza Hanbali
DOI: https://doi.org/10.1017/S1748499521000208, Published online by Cambridge University Press, 17 September 2021 The publisher apologises that upon publication of this article the authors name was swapped around, presenting the surname as their first. The authors correct name is Hamza Hanbali. The online version of this article has been updated. Reference Hanbali, H. (2021). Pricing insurance policies with offsetting relationship. Annals of Actuarial Science, 1-27. doi: 10.1017/S1748499521000208
{"title":"Pricing insurance policies with offsetting relationship – ERRATUM","authors":"Hamza Hanbali","doi":"10.1017/s1748499521000221","DOIUrl":"https://doi.org/10.1017/s1748499521000221","url":null,"abstract":"DOI: https://doi.org/10.1017/S1748499521000208, Published online by Cambridge University Press, 17 September 2021 The publisher apologises that upon publication of this article the authors name was swapped around, presenting the surname as their first. The authors correct name is Hamza Hanbali. The online version of this article has been updated. Reference Hanbali, H. (2021). Pricing insurance policies with offsetting relationship. Annals of Actuarial Science, 1-27. doi: 10.1017/S1748499521000208","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"288 - 288"},"PeriodicalIF":1.7,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46075563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-12DOI: 10.1017/s1748499523000118
Nhan H. Huynh, M. Ludkovski
We investigate jointly modelling age–year-specific rates of various causes of death in a multinational setting. We apply multi-output Gaussian processes (MOGPs), a spatial machine learning method, to smooth and extrapolate multiple cause-of-death mortality rates across several countries and both genders. To maintain flexibility and scalability, we investigate MOGPs with Kronecker-structured kernels and latent factors. In particular, we develop a custom multi-level MOGP that leverages the gridded structure of mortality tables to efficiently capture heterogeneity and dependence across different factor inputs. Results are illustrated with datasets from the Human Cause-of-Death Database (HCD). We discuss a case study involving cancer variations in three European nations and a US-based study that considers eight top-level causes and includes comparison to all-cause analysis. Our models provide insights into the commonality of cause-specific mortality trends and demonstrate the opportunities for respective data fusion.
{"title":"Joint models for cause-of-death mortality in multiple populations","authors":"Nhan H. Huynh, M. Ludkovski","doi":"10.1017/s1748499523000118","DOIUrl":"https://doi.org/10.1017/s1748499523000118","url":null,"abstract":"\u0000 We investigate jointly modelling age–year-specific rates of various causes of death in a multinational setting. We apply multi-output Gaussian processes (MOGPs), a spatial machine learning method, to smooth and extrapolate multiple cause-of-death mortality rates across several countries and both genders. To maintain flexibility and scalability, we investigate MOGPs with Kronecker-structured kernels and latent factors. In particular, we develop a custom multi-level MOGP that leverages the gridded structure of mortality tables to efficiently capture heterogeneity and dependence across different factor inputs. Results are illustrated with datasets from the Human Cause-of-Death Database (HCD). We discuss a case study involving cancer variations in three European nations and a US-based study that considers eight top-level causes and includes comparison to all-cause analysis. Our models provide insights into the commonality of cause-specific mortality trends and demonstrate the opportunities for respective data fusion.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45603244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-03DOI: 10.1017/s1748499521000191
D. Rowell, S. Nghiem, L. Connelly
Abstract Ex post moral hazard arises when the insured has an unobservable influence on the size of a loss after its occurrence. In automobile (property) insurance, ex post moral hazard could increase in the scope of the repairs and/or the value of the repairs. Both vehicle owners and auto repairers could gain from increasing the scope of repairs, while auto repairers would gain from an increase in the value of repairs. An analysis of 994 Australian road traffic crashes found that ex post moral hazard increased the value of repairs by 46.8 per cent of which 9 percentage points was explained by an increase in the scope of the repairs, which was defined as an increased from 2 to 2.4 parts per auto repair.
{"title":"Empirical tests for ex post moral hazard in a market for automobile insurance","authors":"D. Rowell, S. Nghiem, L. Connelly","doi":"10.1017/s1748499521000191","DOIUrl":"https://doi.org/10.1017/s1748499521000191","url":null,"abstract":"Abstract Ex post moral hazard arises when the insured has an unobservable influence on the size of a loss after its occurrence. In automobile (property) insurance, ex post moral hazard could increase in the scope of the repairs and/or the value of the repairs. Both vehicle owners and auto repairers could gain from increasing the scope of repairs, while auto repairers would gain from an increase in the value of repairs. An analysis of 994 Australian road traffic crashes found that ex post moral hazard increased the value of repairs by 46.8 per cent of which 9 percentage points was explained by an increase in the scope of the repairs, which was defined as an increased from 2 to 2.4 parts per auto repair.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"243 - 260"},"PeriodicalIF":1.7,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42736385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.1017/S174849952100021X
C. Dolman, Edward (Jed) Frees, Fei Huang
Although much of the discipline of actuarial science has its roots in isolated mathematicians or small collaborative teams toiling to produce fundamental truths, practice today is frequently geared towards large collaborative teams. In some cases, these teams can cross academic disciplines. In our view, whilst certain matters can be effectively researched within isolated disciplines, others are more suited to multidisciplinary teamwork. Discrimination, particularly data-driven discrimination, is an extremely rich and broad topic. Here, we mainly focus on insurance discrimination in underwriting/pricing, and we use the word “discrimination” in an entirely neutral way, taking it to mean the act of treating distinct groups differently – whether or not such discrimination can be justified based on legal, economic or ethical grounds. Whilst narrow research into this subject is certainly possible, a broad perspective is likely to be beneficial in creating robust, well-considered solutions to actual or perceived problems. Significant harms can and, indeed, have been caused by well-intended but narrowly framed solutions to large, difficult problems. In discrimination, for example, the intuitively appealing “fairness through unawareness” is known to make overall discrimination worse in some circumstances (for a worked example, see Reid & O’Callaghan 2018). Whilst the unawareness problem has been understood in the computer science community for some time (see, e.g. Pedreschi et al. 2008), it is an idea still embedded in many laws around the world, and too frequently seen by some as a solution for data-driven discrimination. As with other institutions, insurers are redefining the way that they do business with the increasing capacity and computational abilities of computers, availability of new and innovative sources of data, and advanced artificial intelligence algorithms that can detect patterns in data that were previously unknown. Conceptually, Big Data and new technologies do not alter the fundamental issues of insurance discrimination; one can think of credit-based insurance scoring and price optimization as simply forerunners of this movement. Yet, old challenges may becomemore prominent in this rapidly developing landscape. Issues regarding privacy and the use of algorithmic proxies take on increased importance as insurers’ extensive use of data and computational abilities evolve. Actuaries need to be attuned to these issues and, ideally, involved in proposals to address them. For example, Frees & Huang (2021) draw upon historical, economic, legal, and computer science literatures to understand insurance discrimination. In particular, they review social and economic principles that can be used to assess whether insurance discrimination is ethical or is “unfair” and morally indefensible in some sense, examine insurance regulations and laws across different lines of business and jurisdictions, and explore the machine learning literature on mitigating
{"title":"Multidisciplinary collaboration on discrimination – not just “Nice to Have”","authors":"C. Dolman, Edward (Jed) Frees, Fei Huang","doi":"10.1017/S174849952100021X","DOIUrl":"https://doi.org/10.1017/S174849952100021X","url":null,"abstract":"Although much of the discipline of actuarial science has its roots in isolated mathematicians or small collaborative teams toiling to produce fundamental truths, practice today is frequently geared towards large collaborative teams. In some cases, these teams can cross academic disciplines. In our view, whilst certain matters can be effectively researched within isolated disciplines, others are more suited to multidisciplinary teamwork. Discrimination, particularly data-driven discrimination, is an extremely rich and broad topic. Here, we mainly focus on insurance discrimination in underwriting/pricing, and we use the word “discrimination” in an entirely neutral way, taking it to mean the act of treating distinct groups differently – whether or not such discrimination can be justified based on legal, economic or ethical grounds. Whilst narrow research into this subject is certainly possible, a broad perspective is likely to be beneficial in creating robust, well-considered solutions to actual or perceived problems. Significant harms can and, indeed, have been caused by well-intended but narrowly framed solutions to large, difficult problems. In discrimination, for example, the intuitively appealing “fairness through unawareness” is known to make overall discrimination worse in some circumstances (for a worked example, see Reid & O’Callaghan 2018). Whilst the unawareness problem has been understood in the computer science community for some time (see, e.g. Pedreschi et al. 2008), it is an idea still embedded in many laws around the world, and too frequently seen by some as a solution for data-driven discrimination. As with other institutions, insurers are redefining the way that they do business with the increasing capacity and computational abilities of computers, availability of new and innovative sources of data, and advanced artificial intelligence algorithms that can detect patterns in data that were previously unknown. Conceptually, Big Data and new technologies do not alter the fundamental issues of insurance discrimination; one can think of credit-based insurance scoring and price optimization as simply forerunners of this movement. Yet, old challenges may becomemore prominent in this rapidly developing landscape. Issues regarding privacy and the use of algorithmic proxies take on increased importance as insurers’ extensive use of data and computational abilities evolve. Actuaries need to be attuned to these issues and, ideally, involved in proposals to address them. For example, Frees & Huang (2021) draw upon historical, economic, legal, and computer science literatures to understand insurance discrimination. In particular, they review social and economic principles that can be used to assess whether insurance discrimination is ethical or is “unfair” and morally indefensible in some sense, examine insurance regulations and laws across different lines of business and jurisdictions, and explore the machine learning literature on mitigating ","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"15 1","pages":"485 - 487"},"PeriodicalIF":1.7,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46755661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cole van Jaarsveldt, M. Ames, Gareth W. Peters, M. Chantler
Abstract This work presents a $textsf{Python}$ EMD package named AdvEMDpy that is both more flexible and generalises existing empirical mode decomposition (EMD) packages in $textsf{Python}$ , $textsf{R}$ , and $textsf{MATLAB}$ . It is aimed specifically for use by the insurance and financial risk communities, for applications such as return modelling, claims modelling, and life insurance applications with a particular focus on mortality modelling. AdvEMDpy both expands upon the EMD options and methods available, and improves their statistical robustness and efficiency, providing a robust, usable, and reliable toolbox. Unlike many EMD packages, AdvEMDpy allows customisation by the user, to ensure that a broader class of linear, non-linear, and non-stationary time series analyses can be performed. The intrinsic mode functions (IMFs) extracted using EMD contain complex multi-frequency structures which warrant maximum algorithmic customisation for effective analysis. A major contribution of this package is the intensive treatment of the EMD edge effect which is the most ubiquitous problem in EMD and time series analysis. Various EMD techniques, of varying intricacy from numerous works, have been developed, refined, and, for the first time, compiled in AdvEMDpy. In addition to the EMD edge effect, numerous pre-processing, post-processing, detrended fluctuation analysis (localised trend estimation) techniques, stopping criteria, spline methods, discrete-time Hilbert transforms (DTHT), knot point optimisations, and other algorithmic variations have been incorporated and presented to the users of AdvEMDpy. This paper and the supplementary materials provide several real-world actuarial applications of this package for the user’s benefit.
{"title":"Package AdvEMDpy: Algorithmic variations of empirical mode decomposition in Python","authors":"Cole van Jaarsveldt, M. Ames, Gareth W. Peters, M. Chantler","doi":"10.2139/ssrn.3947132","DOIUrl":"https://doi.org/10.2139/ssrn.3947132","url":null,"abstract":"Abstract This work presents a \u0000$textsf{Python}$\u0000 EMD package named AdvEMDpy that is both more flexible and generalises existing empirical mode decomposition (EMD) packages in \u0000$textsf{Python}$\u0000 , \u0000$textsf{R}$\u0000 , and \u0000$textsf{MATLAB}$\u0000 . It is aimed specifically for use by the insurance and financial risk communities, for applications such as return modelling, claims modelling, and life insurance applications with a particular focus on mortality modelling. AdvEMDpy both expands upon the EMD options and methods available, and improves their statistical robustness and efficiency, providing a robust, usable, and reliable toolbox. Unlike many EMD packages, AdvEMDpy allows customisation by the user, to ensure that a broader class of linear, non-linear, and non-stationary time series analyses can be performed. The intrinsic mode functions (IMFs) extracted using EMD contain complex multi-frequency structures which warrant maximum algorithmic customisation for effective analysis. A major contribution of this package is the intensive treatment of the EMD edge effect which is the most ubiquitous problem in EMD and time series analysis. Various EMD techniques, of varying intricacy from numerous works, have been developed, refined, and, for the first time, compiled in AdvEMDpy. In addition to the EMD edge effect, numerous pre-processing, post-processing, detrended fluctuation analysis (localised trend estimation) techniques, stopping criteria, spline methods, discrete-time Hilbert transforms (DTHT), knot point optimisations, and other algorithmic variations have been incorporated and presented to the users of AdvEMDpy. This paper and the supplementary materials provide several real-world actuarial applications of this package for the user’s benefit.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"59 1","pages":"606 - 642"},"PeriodicalIF":1.7,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86455179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-17DOI: 10.1017/S1748499521000208
Hamza Hanbali
Abstract This paper investigates the benefits of incorporating diversification effects into the pricing process of insurance policies from two different business lines. The paper shows that, for the same risk reduction, insurers pricing policies jointly can have a competitive advantage over those pricing them separately. However, the choice of competitiveness constrains the underwriting flexibility of joint pricers. The paper goes a step further by modelling explicitly the relationship between premiums and the number of customers in each line. Using the total collected premiums as a criterion to compare the competing strategies, the paper provides conditions for the optimal pricing decision based on policyholders’ sensitivity to price discounts. The results are illustrated for a portfolio of annuities and assurances. Further, using non-life data from the Brazilian insurance market, an empirical exploration shows that most pairs satisfy the condition for being priced jointly, even when pairwise correlations are high.
{"title":"Pricing insurance policies with offsetting relationship","authors":"Hamza Hanbali","doi":"10.1017/S1748499521000208","DOIUrl":"https://doi.org/10.1017/S1748499521000208","url":null,"abstract":"Abstract This paper investigates the benefits of incorporating diversification effects into the pricing process of insurance policies from two different business lines. The paper shows that, for the same risk reduction, insurers pricing policies jointly can have a competitive advantage over those pricing them separately. However, the choice of competitiveness constrains the underwriting flexibility of joint pricers. The paper goes a step further by modelling explicitly the relationship between premiums and the number of customers in each line. Using the total collected premiums as a criterion to compare the competing strategies, the paper provides conditions for the optimal pricing decision based on policyholders’ sensitivity to price discounts. The results are illustrated for a portfolio of annuities and assurances. Further, using non-life data from the Brazilian insurance market, an empirical exploration shows that most pairs satisfy the condition for being priced jointly, even when pairwise correlations are high.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"48 1","pages":"261 - 287"},"PeriodicalIF":1.7,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57010062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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