Pub Date : 2022-01-24DOI: 10.1080/03461238.2021.2025145
Yuxuan Liu, Zhengjun Jiang, Yixin Qu
ABSTRACT When an insurance company's risk reserve is governed by a Markov-modulated jump-diffusion risk model, we study gambler's ruin problem in terms of two-sided ruin probability that the insurance company shall be ruined before its risk reserve reaches an upper barrier level . We employ Banach contraction principle and q-scale functions to confirm the two-sided ruin probability to be the only fixed point of a contraction mapping and construct an iterative algorithm of approximating the two-sided ruin probability. We find that the two-sided ruin probability and Lipschitz constant in the contraction mapping depend on the upper barrier level b, premium rate per squared volatility, Markov intensity rate per squared volatility, Poisson intensity rate per squared volatility and the mean value of claim per unit of time. Finally, we present a numerical example with two regimes to show the efficiency of the iterative algorithm.
{"title":"Gambler's ruin problem in a Markov-modulated jump-diffusion risk model","authors":"Yuxuan Liu, Zhengjun Jiang, Yixin Qu","doi":"10.1080/03461238.2021.2025145","DOIUrl":"https://doi.org/10.1080/03461238.2021.2025145","url":null,"abstract":"ABSTRACT When an insurance company's risk reserve is governed by a Markov-modulated jump-diffusion risk model, we study gambler's ruin problem in terms of two-sided ruin probability that the insurance company shall be ruined before its risk reserve reaches an upper barrier level . We employ Banach contraction principle and q-scale functions to confirm the two-sided ruin probability to be the only fixed point of a contraction mapping and construct an iterative algorithm of approximating the two-sided ruin probability. We find that the two-sided ruin probability and Lipschitz constant in the contraction mapping depend on the upper barrier level b, premium rate per squared volatility, Markov intensity rate per squared volatility, Poisson intensity rate per squared volatility and the mean value of claim per unit of time. Finally, we present a numerical example with two regimes to show the efficiency of the iterative algorithm.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87567378","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 : 2022-01-24DOI: 10.1080/03461238.2022.2025891
S. Richards
ABSTRACT Mortality levels vary by benefit amount, and a common simplification is to group by non-overlapping ranges of varying widths. However, this ignores the continuous nature of benefit amounts and leads to discretisation error, i.e. heterogeneity within benefit ranges and step jumps at range boundaries. Another drawback of discretisation is that fitted parameters are not easily extrapolated to values outside the range of the experience data. To address these shortcomings it is often better to model mortality continuously by benefit amount. In this paper we present a method of modelling mortality levels continuously by a financial covariate such as pension size. We split the task into (i) a transform function to address the presence of extreme benefit amounts in actuarial data sets, and (ii) a response function to model mortality. Using as few as two parameters, the method avoids discretisation error and extrapolates to amounts outside the range covered by the calibrating data set. We illustrate the method by applying it to seven international data sets of pensioners and annuitants.
{"title":"Modelling mortality by continuous benefit amount","authors":"S. Richards","doi":"10.1080/03461238.2022.2025891","DOIUrl":"https://doi.org/10.1080/03461238.2022.2025891","url":null,"abstract":"ABSTRACT Mortality levels vary by benefit amount, and a common simplification is to group by non-overlapping ranges of varying widths. However, this ignores the continuous nature of benefit amounts and leads to discretisation error, i.e. heterogeneity within benefit ranges and step jumps at range boundaries. Another drawback of discretisation is that fitted parameters are not easily extrapolated to values outside the range of the experience data. To address these shortcomings it is often better to model mortality continuously by benefit amount. In this paper we present a method of modelling mortality levels continuously by a financial covariate such as pension size. We split the task into (i) a transform function to address the presence of extreme benefit amounts in actuarial data sets, and (ii) a response function to model mortality. Using as few as two parameters, the method avoids discretisation error and extrapolates to amounts outside the range covered by the calibrating data set. We illustrate the method by applying it to seven international data sets of pensioners and annuitants.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81195164","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 : 2022-01-04DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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