Pub Date : 2022-01-04DOI: 10.1080/03461238.2021.2020892
J. Pinquet
ABSTRACT Nonnegative linear filtering of nonnegative risk variables necessitates positivity properties on the variance–covariance matrices of random effects, if experience rating is derived from mixture models. A variance–covariance matrix is a potential if it is nonsingular and if its inverse is diagonally dominant, with off-diagonal entries that are all nonpositive. We consider risk models with stationary random effects whose variance–covariance matrices are potentials. Positive credibility predictors of nonnegative risks are obtained from these mixture models. The set of variance–covariance matrices that are potentials is closed under extraction of principal submatrices. This strong hereditary property maintains the positivity of the affine predictor if the horizon is greater than one and if the history is lacunary. The specifications of the dynamic random effects presented in this paper fulfill the required positivity properties, and encompass the three possible levels for the length of memory in the mixing distribution. A case study discusses the possible strategies in the prediction of the pure premium from dynamic random effects.
{"title":"Hereditarity of potential matrices and positive affine prediction of nonnegative risks from mixture models","authors":"J. Pinquet","doi":"10.1080/03461238.2021.2020892","DOIUrl":"https://doi.org/10.1080/03461238.2021.2020892","url":null,"abstract":"ABSTRACT Nonnegative linear filtering of nonnegative risk variables necessitates positivity properties on the variance–covariance matrices of random effects, if experience rating is derived from mixture models. A variance–covariance matrix is a potential if it is nonsingular and if its inverse is diagonally dominant, with off-diagonal entries that are all nonpositive. We consider risk models with stationary random effects whose variance–covariance matrices are potentials. Positive credibility predictors of nonnegative risks are obtained from these mixture models. The set of variance–covariance matrices that are potentials is closed under extraction of principal submatrices. This strong hereditary property maintains the positivity of the affine predictor if the horizon is greater than one and if the history is lacunary. The specifications of the dynamic random effects presented in this paper fulfill the required positivity properties, and encompass the three possible levels for the length of memory in the mixing distribution. A case study discusses the possible strategies in the prediction of the pure premium from dynamic random effects.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"90 1","pages":"659 - 681"},"PeriodicalIF":1.8,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91164593","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 : 2021-12-21DOI: 10.1080/03461238.2022.2079996
M. Christiansen
ABSTRACT Current reporting standards for insurers require a decomposition of observed profits and losses in such a way that changes in the insurer's balance sheet can be attributed to specified risk factors. Generating such a decomposition is a non-trivial task because balance sheets generally depend on the risk factors in a non-linear way. This paper starts from an axiomatic perspective on profit and loss decompositions and finds that the axioms necessarily lead to infinitesimal sequential updating (ISU) decompositions, provided that the latter exist and are stable, whereas the current practice is rather to use sequential updating (SU) decompositions. The generality of the axiomatic approach makes the results useful also beyond insurance applications wherever profits and losses shall be additively decomposed in a risk-oriented manner.
{"title":"On the decomposition of an insurer's profits and losses","authors":"M. Christiansen","doi":"10.1080/03461238.2022.2079996","DOIUrl":"https://doi.org/10.1080/03461238.2022.2079996","url":null,"abstract":"ABSTRACT Current reporting standards for insurers require a decomposition of observed profits and losses in such a way that changes in the insurer's balance sheet can be attributed to specified risk factors. Generating such a decomposition is a non-trivial task because balance sheets generally depend on the risk factors in a non-linear way. This paper starts from an axiomatic perspective on profit and loss decompositions and finds that the axioms necessarily lead to infinitesimal sequential updating (ISU) decompositions, provided that the latter exist and are stable, whereas the current practice is rather to use sequential updating (SU) decompositions. The generality of the axiomatic approach makes the results useful also beyond insurance applications wherever profits and losses shall be additively decomposed in a risk-oriented manner.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"283 1","pages":"51 - 70"},"PeriodicalIF":1.8,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76833615","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 : 2021-12-13DOI: 10.1080/03461238.2022.2089050
Ling Wang, Mei Choi Chiu, H. Y. Wong
This paper investigates the time-consistent mean-variance reinsurance-investment (RI) problem faced by life insurers. Inspired by recent findings that mortality rates exhibit long-range dependence (LRD), we examine the effect of LRD on RI strategies. We adopt the Volterra mortality model proposed in Wang et al. [(2021). Volterra mortality model: actuarial valuation and risk management with long-range dependence. Insurance: Mathematics and Economics 96, 1–14] to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with intensity represented by the stochastic mortality rate. Under the open-loop equilibrium mean-variance criterion, we derive explicit equilibrium RI controls and study the uniqueness of these controls in cases of constant and state-dependent risk aversion. We simultaneously resolve difficulties arising from unbounded non-Markovian parameters and sudden increases in the insurer's wealth process. While the exiting literature suggests that LRD has a significant effect on longevity hedging, we find that reinsurance is a risk management strategy that is robust to LRD.
{"title":"Time-consistent mean-variance reinsurance-investment problem with long-range dependent mortality rate","authors":"Ling Wang, Mei Choi Chiu, H. Y. Wong","doi":"10.1080/03461238.2022.2089050","DOIUrl":"https://doi.org/10.1080/03461238.2022.2089050","url":null,"abstract":"This paper investigates the time-consistent mean-variance reinsurance-investment (RI) problem faced by life insurers. Inspired by recent findings that mortality rates exhibit long-range dependence (LRD), we examine the effect of LRD on RI strategies. We adopt the Volterra mortality model proposed in Wang et al. [(2021). Volterra mortality model: actuarial valuation and risk management with long-range dependence. Insurance: Mathematics and Economics 96, 1–14] to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with intensity represented by the stochastic mortality rate. Under the open-loop equilibrium mean-variance criterion, we derive explicit equilibrium RI controls and study the uniqueness of these controls in cases of constant and state-dependent risk aversion. We simultaneously resolve difficulties arising from unbounded non-Markovian parameters and sudden increases in the insurer's wealth process. While the exiting literature suggests that LRD has a significant effect on longevity hedging, we find that reinsurance is a risk management strategy that is robust to LRD.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"60 1","pages":"123 - 152"},"PeriodicalIF":1.8,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89083973","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 : 2021-11-25DOI: 10.1080/03461238.2022.2049636
Julian Jetses, M. Christiansen
ABSTRACT In with-profit life insurance, the prudent valuation of future insurance liabilities leads to systematic surplus that mainly belongs to the policyholders and is redistributed as bonus. For a fair and lawful redistribution of surplus, the insurer needs to decompose the total portfolio surplus with respect to the contributions of individual policies and with respect to different risk sources. For this task, actuaries have a number of heuristic decomposition formulas, but an overarching decomposition principle is still missing. This paper fills that gap by introducing a so-called ISU decomposition principle that bases on infinitesimal sequential updates of the insurer's valuation basis. It is shown that the existing heuristic decomposition formulas can be replicated as ISU decompositions. Furthermore, alternative decomposition principles and their relation to the ISU decomposition principle are discussed. The generality of the ISU concept makes it a useful tool also beyond classical surplus decompositions in life insurance.
{"title":"A general surplus decomposition principle in life insurance","authors":"Julian Jetses, M. Christiansen","doi":"10.1080/03461238.2022.2049636","DOIUrl":"https://doi.org/10.1080/03461238.2022.2049636","url":null,"abstract":"ABSTRACT In with-profit life insurance, the prudent valuation of future insurance liabilities leads to systematic surplus that mainly belongs to the policyholders and is redistributed as bonus. For a fair and lawful redistribution of surplus, the insurer needs to decompose the total portfolio surplus with respect to the contributions of individual policies and with respect to different risk sources. For this task, actuaries have a number of heuristic decomposition formulas, but an overarching decomposition principle is still missing. This paper fills that gap by introducing a so-called ISU decomposition principle that bases on infinitesimal sequential updates of the insurer's valuation basis. It is shown that the existing heuristic decomposition formulas can be replicated as ISU decompositions. Furthermore, alternative decomposition principles and their relation to the ISU decomposition principle are discussed. The generality of the ISU concept makes it a useful tool also beyond classical surplus decompositions in life insurance.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"49 1","pages":"901 - 925"},"PeriodicalIF":1.8,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74099962","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 : 2021-11-24DOI: 10.1080/03461238.2021.2002185
Stig. I. Rosenlund
Jewell's credibility model with two hierarchical levels and three variance parameters is treated. Under some additional assumptions, new pseudo-estimators are deduced, i.e. estimators which are defined by expressions that contain the estimands themselves and which must be solved numerically, for the parameters for variation between groups within sector and for variation between sectors. A Tweedie model is assumed for conditional claim rates, with exponent either 1 or 2, where 1 is for conditionally Poisson claim frequencies and 2 is for mean claim severities. Simulation results, where some of the additional assumptions are violated, indicate that our new pseudo-estimators are preferable over previous pseudo-estimators and non-pseudo-estimators for many cases that can be identified. The new between-sectors estimator seems to be universally better than the previous estimators. The goodness-of-fit of an estimator is measured by the square root of its mean square error relative to the true parameter.
{"title":"Hierarchical credibility pseudo-estimators","authors":"Stig. I. Rosenlund","doi":"10.1080/03461238.2021.2002185","DOIUrl":"https://doi.org/10.1080/03461238.2021.2002185","url":null,"abstract":"Jewell's credibility model with two hierarchical levels and three variance parameters is treated. Under some additional assumptions, new pseudo-estimators are deduced, i.e. estimators which are defined by expressions that contain the estimands themselves and which must be solved numerically, for the parameters for variation between groups within sector and for variation between sectors. A Tweedie model is assumed for conditional claim rates, with exponent either 1 or 2, where 1 is for conditionally Poisson claim frequencies and 2 is for mean claim severities. Simulation results, where some of the additional assumptions are violated, indicate that our new pseudo-estimators are preferable over previous pseudo-estimators and non-pseudo-estimators for many cases that can be identified. The new between-sectors estimator seems to be universally better than the previous estimators. The goodness-of-fit of an estimator is measured by the square root of its mean square error relative to the true parameter.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"82 1","pages":"552 - 564"},"PeriodicalIF":1.8,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90233391","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 : 2021-11-16DOI: 10.1080/03461238.2021.1998922
T. Boonen, Yiying Zhang
Bowley reinsurance solutions are reinsurance contracts for which the reinsurer optimally sets the pricing density while anticipating that the insurer will choose the optimal reinsurance indemnity given this pricing density. This Bowley solution concept of equilibrium reinsurance strategy has been revisited in the modern risk management framework by Boonen et al. [(2021). Bowley reinsurance with asymmetric information on the insurer's risk preferences. Scandinavian Actuarial Journal 2021, 623–644], where the insurer and reinsurer are both endowed with distortion risk measures but there is asymmetric information on the distortion risk measure of the insurer. In this article, we continue to study this framework, but we allow the premium principle to be more flexible. We call this solution the first-best Bowley solution. We provide first-best Bowley solutions in closed form under very general assumptions. We implement some numerical examples to illustrate the findings and the comparisons with the second-best solution. The main result is further extended to the case when both the reinsurer and the insurers have heterogeneous beliefs on the distribution functions of the underlying risk.
{"title":"Bowley reinsurance with asymmetric information: a first-best solution","authors":"T. Boonen, Yiying Zhang","doi":"10.1080/03461238.2021.1998922","DOIUrl":"https://doi.org/10.1080/03461238.2021.1998922","url":null,"abstract":"Bowley reinsurance solutions are reinsurance contracts for which the reinsurer optimally sets the pricing density while anticipating that the insurer will choose the optimal reinsurance indemnity given this pricing density. This Bowley solution concept of equilibrium reinsurance strategy has been revisited in the modern risk management framework by Boonen et al. [(2021). Bowley reinsurance with asymmetric information on the insurer's risk preferences. Scandinavian Actuarial Journal 2021, 623–644], where the insurer and reinsurer are both endowed with distortion risk measures but there is asymmetric information on the distortion risk measure of the insurer. In this article, we continue to study this framework, but we allow the premium principle to be more flexible. We call this solution the first-best Bowley solution. We provide first-best Bowley solutions in closed form under very general assumptions. We implement some numerical examples to illustrate the findings and the comparisons with the second-best solution. The main result is further extended to the case when both the reinsurer and the insurers have heterogeneous beliefs on the distribution functions of the underlying risk.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"18 1","pages":"532 - 551"},"PeriodicalIF":1.8,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72646351","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 : 2021-11-16DOI: 10.1080/03461238.2021.1995781
J. Akahori, C. Constantinescu, Y. Imamura, H. Pham
Inspired by the double-debt problem in Japan where the mortgagor has to pay the remaining loan even if their house was destroyed by a catastrophic event, we model the lender's cash flow, by an exponential functional of a renewal-reward process. We propose an insurance add-on to the loan repayments and analyse the asymptotic behavior of the distribution of the first hitting time, which represents the probability of full repayment. We show that the finite-time probability of full loan repayment converges exponentially fast to the infinite-time one. In a few concrete scenarios, we calculate the exact form of the infinite-time probability and the corresponding premiums.
{"title":"An application of risk theory to mortgage lending","authors":"J. Akahori, C. Constantinescu, Y. Imamura, H. Pham","doi":"10.1080/03461238.2021.1995781","DOIUrl":"https://doi.org/10.1080/03461238.2021.1995781","url":null,"abstract":"Inspired by the double-debt problem in Japan where the mortgagor has to pay the remaining loan even if their house was destroyed by a catastrophic event, we model the lender's cash flow, by an exponential functional of a renewal-reward process. We propose an insurance add-on to the loan repayments and analyse the asymptotic behavior of the distribution of the first hitting time, which represents the probability of full repayment. We show that the finite-time probability of full loan repayment converges exponentially fast to the infinite-time one. In a few concrete scenarios, we calculate the exact form of the infinite-time probability and the corresponding premiums.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"58 1","pages":"447 - 469"},"PeriodicalIF":1.8,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86764727","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 : 2021-11-09DOI: 10.1080/03461238.2021.1997795
Yuxin Zhou, M. Sherris, Jonathan Ziveyi, Mengyi Xu
There is a significant potential demand around the world for a flexible product to manage individual longevity risk. However, annuity markets remain thin, driven by factors including lack of pricing transparency, high product loadings, bequest motives, loss aversion, and the difficulty to hedge the risk. This paper proposes an individual retirement product to allow flexible management of longevity risk. The product combines a lifetime income with a flexible death benefit to meet individual bequest needs. It also benefits the issuers by lower mortality risk due to the natural hedging, and thus lower capital cost as a risk margin. We apply actuarial models that provide transparent pricing for interest rate and mortality risk, the construction of immunized bond portfolios, and the determination of a loading and solvency margin for systematic longevity risk. We also quantify the natural hedging benefits arising from the flexible inclusion of both survival benefits and death benefits.
{"title":"An innovative design of flexible, bequest-enhanced life annuity with natural hedging","authors":"Yuxin Zhou, M. Sherris, Jonathan Ziveyi, Mengyi Xu","doi":"10.1080/03461238.2021.1997795","DOIUrl":"https://doi.org/10.1080/03461238.2021.1997795","url":null,"abstract":"There is a significant potential demand around the world for a flexible product to manage individual longevity risk. However, annuity markets remain thin, driven by factors including lack of pricing transparency, high product loadings, bequest motives, loss aversion, and the difficulty to hedge the risk. This paper proposes an individual retirement product to allow flexible management of longevity risk. The product combines a lifetime income with a flexible death benefit to meet individual bequest needs. It also benefits the issuers by lower mortality risk due to the natural hedging, and thus lower capital cost as a risk margin. We apply actuarial models that provide transparent pricing for interest rate and mortality risk, the construction of immunized bond portfolios, and the determination of a loading and solvency margin for systematic longevity risk. We also quantify the natural hedging benefits arising from the flexible inclusion of both survival benefits and death benefits.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"45 1","pages":"488 - 509"},"PeriodicalIF":1.8,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89867254","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 : 2021-10-31DOI: 10.1080/03461238.2022.2097019
Martin Bladt, Jorge Yslas
ABSTRACT The task of modeling claim severities is addressed when data is not consistent with the classical regression assumptions. This framework is common in several lines of business within insurance and reinsurance, where catastrophic losses or heterogeneous sub-populations result in data difficult to model. Their correct analysis is required for pricing insurance products, and some of the most prevalent recent specifications in this direction are mixture-of-experts models. This paper proposes a regression model that generalizes the latter approach to the phase-type distribution setting. More specifically, the concept of mixing is extended to the case where an entire Markov jump process is unobserved and where states can communicate with each other. The covariates then act on the initial probabilities of such underlying chain, which play the role of expert weights. The basic properties of such a model are computed in terms of matrix functionals, and denseness properties are derived, demonstrating their flexibility. An effective estimation procedure is proposed, based on the EM algorithm and multinomial logistic regression, and subsequently illustrated using simulated and real-world datasets. The increased flexibility of the proposed models does not come at a high computational cost, and the motivation and interpretation are equally transparent to simpler MoE models.
{"title":"Phase-type mixture-of-experts regression for loss severities","authors":"Martin Bladt, Jorge Yslas","doi":"10.1080/03461238.2022.2097019","DOIUrl":"https://doi.org/10.1080/03461238.2022.2097019","url":null,"abstract":"ABSTRACT The task of modeling claim severities is addressed when data is not consistent with the classical regression assumptions. This framework is common in several lines of business within insurance and reinsurance, where catastrophic losses or heterogeneous sub-populations result in data difficult to model. Their correct analysis is required for pricing insurance products, and some of the most prevalent recent specifications in this direction are mixture-of-experts models. This paper proposes a regression model that generalizes the latter approach to the phase-type distribution setting. More specifically, the concept of mixing is extended to the case where an entire Markov jump process is unobserved and where states can communicate with each other. The covariates then act on the initial probabilities of such underlying chain, which play the role of expert weights. The basic properties of such a model are computed in terms of matrix functionals, and denseness properties are derived, demonstrating their flexibility. An effective estimation procedure is proposed, based on the EM algorithm and multinomial logistic regression, and subsequently illustrated using simulated and real-world datasets. The increased flexibility of the proposed models does not come at a high computational cost, and the motivation and interpretation are equally transparent to simpler MoE models.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"20 1","pages":"303 - 329"},"PeriodicalIF":1.8,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81811413","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 : 2021-10-28DOI: 10.1080/03461238.2021.1992001
Vanessa Hanna, P. Hieber, P. Devolder
In many countries, the decline in interest rates has reduced the interest in traditional participating life insurance contracts with investment guarantees and has led to a shift to unit-linked policies without guarantees. We design a novel mixed insurance contract splitting premium payments between a participating and a unit-linked fund. An additional guarantee fee is applied on the unit-linked return in order to increase the investment guarantee of the participating fund. In a utility-based framework, using power utility and prospect theory as preference functions, we show that the mixed product is usually perceived more attractive than a full investment in either the unit-linked or the participating contract. The guarantee fee is beneficial for conservative investors interested in stronger protection against losses. This is also interesting from a marketing perspective: By the increase of the guarantee in the participating product, zero or negative guaranteed rates can be avoided.
{"title":"Mixed participating and unit-linked life insurance contracts: design, pricing and optimal strategy","authors":"Vanessa Hanna, P. Hieber, P. Devolder","doi":"10.1080/03461238.2021.1992001","DOIUrl":"https://doi.org/10.1080/03461238.2021.1992001","url":null,"abstract":"In many countries, the decline in interest rates has reduced the interest in traditional participating life insurance contracts with investment guarantees and has led to a shift to unit-linked policies without guarantees. We design a novel mixed insurance contract splitting premium payments between a participating and a unit-linked fund. An additional guarantee fee is applied on the unit-linked return in order to increase the investment guarantee of the participating fund. In a utility-based framework, using power utility and prospect theory as preference functions, we show that the mixed product is usually perceived more attractive than a full investment in either the unit-linked or the participating contract. The guarantee fee is beneficial for conservative investors interested in stronger protection against losses. This is also interesting from a marketing perspective: By the increase of the guarantee in the participating product, zero or negative guaranteed rates can be avoided.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"28 1","pages":"421 - 446"},"PeriodicalIF":1.8,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84800683","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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