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Reserve-dependent Management Actions in life insurance 人寿保险中依赖储备的管理行为
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-04-25 DOI: 10.1080/03461238.2022.2061868
D. Falden, Anna Kamille Nyegaard
{"title":"Reserve-dependent Management Actions in life insurance","authors":"D. Falden, Anna Kamille Nyegaard","doi":"10.1080/03461238.2022.2061868","DOIUrl":"https://doi.org/10.1080/03461238.2022.2061868","url":null,"abstract":"In a set-up of with-profit life insurance including bonus, we study the calculation of the market reserve, where Management Actions such as investment strategies and bonus allocation strategies depend on the reserve itself. Since the amount of future bonus depends on the retrospective savings account, the introduction of Management Actions that depend on the prospective market reserve results in an entanglement of retrospective and prospective reserves. We study the complications that arise due to the interdependence between retrospective and prospective reserves, and characterize the market reserve by a partial differential equation (PDE). We reduce the dimension of the PDE in the case of linearity, and furthermore, we suggest an approximation of the market reserve based on the forward rate. The quality of the approximation is studied in a numerical example.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"11 1","pages":"1 - 19"},"PeriodicalIF":1.8,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84765592","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}
引用次数: 0
Variable annuity pricing, valuation, and risk management: a survey 可变年金定价、估值与风险管理:一项调查
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-03-28 DOI: 10.1080/03461238.2022.2049635
Runhuan Feng, Guojun Gan, Ning Zhang
{"title":"Variable annuity pricing, valuation, and risk management: a survey","authors":"Runhuan Feng, Guojun Gan, Ning Zhang","doi":"10.1080/03461238.2022.2049635","DOIUrl":"https://doi.org/10.1080/03461238.2022.2049635","url":null,"abstract":"Variable annuity is arguably the most complex individual retirement planning product in the financial market. Its intricacy stems from a variety of product features including investment options, guaranteed benefits, withdrawal options, etc. In many ways, variable annuities can be viewed as traditional life and annuity products at the next level of sophistication with added financial options. Despite a significant amount of publications by practitioners and academics on the subject matter, there have been few research papers that systematically exploit the basic principles underlying the operation of variable annuities. This survey paper aims to fill in the gap in the literature for an overview of state-of-the-art technology and recent trends in the development of variable annuities.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"22 1","pages":"867 - 900"},"PeriodicalIF":1.8,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81599946","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}
引用次数: 10
On the surplus management of funds with assets and liabilities in presence of solvency requirements 关于资金盈余管理与资产负债存在偿付能力要求
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-03-10 DOI: 10.1080/03461238.2022.2116725
Benjamin Avanzi, Pingfu Chen, L. Henriksen, Bernard Wong
{"title":"On the surplus management of funds with assets and liabilities in presence of solvency requirements","authors":"Benjamin Avanzi, Pingfu Chen, L. Henriksen, Bernard Wong","doi":"10.1080/03461238.2022.2116725","DOIUrl":"https://doi.org/10.1080/03461238.2022.2116725","url":null,"abstract":"In this paper, we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu [(2003). Geometric Brownian motion models for assets and liabilities: From pension funding to optimal dividends. North American Actuarial Journal 7(3), 37–56]. We determine what dividend strategy maximises the expected present value of dividends until ruin in two cases: (i) when shareholders won't cover surplus shortfalls and a solvency constraint [as in Paulsen (2003). Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics 7(4), 457–473] is consequently imposed and (ii) when shareholders are always to fund any capital deficiency with capital (asset) injections. In the latter case, ruin will never occur and the objective is to maximise the difference between dividends and capital injections. Developing and using appropriate verification lemmas, we show that the optimal dividend strategy is, in both cases, of barrier type. Both value functions are derived in closed form. Furthermore, the barrier is defined on the ratio of assets to liabilities, which mimics some of the dividend strategies that can be observed in practice by insurance companies. The existence and uniqueness of the optimal strategies are shown. Results are illustrated.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"119 1","pages":"477 - 508"},"PeriodicalIF":1.8,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77963737","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}
引用次数: 0
Analytic valuation of GMDB options with utility based asset allocation 基于效用的资产配置GMDB期权分析估值
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-03-09 DOI: 10.1080/03461238.2022.2034127
Eric R. Ulm
{"title":"Analytic valuation of GMDB options with utility based asset allocation","authors":"Eric R. Ulm","doi":"10.1080/03461238.2022.2034127","DOIUrl":"https://doi.org/10.1080/03461238.2022.2034127","url":null,"abstract":"A number of analytic solutions have been found for Variable Annuity Guaranteed Minimum Death Benefit (GMDB) option values under a variety of mortality laws. To date, the solutions are for Risk-Neutral valuation only. Where policyholder decisions are allowed, it is assumed that they act to maximize the risk-neutral value of the GMDB. We examine situations where the asset allocation decisions are made to maximize expected utility rather than option value. We find analytic solutions for both return of premium and ratchet options at small values of bequest motive for a number of mortality laws.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"7 1","pages":"816 - 840"},"PeriodicalIF":1.8,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84676775","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}
引用次数: 1
Optimal reinsurance pricing with ambiguity aversion and relative performance concerns in the principal-agent model 委托代理模型中具有歧义规避和相对绩效关注的最优再保险定价
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-02-24 DOI: 10.1080/03461238.2022.2026459
Ailing Gu, Shumin Chen, Zhongfei Li, F. Viens
{"title":"Optimal reinsurance pricing with ambiguity aversion and relative performance concerns in the principal-agent model","authors":"Ailing Gu, Shumin Chen, Zhongfei Li, F. Viens","doi":"10.1080/03461238.2022.2026459","DOIUrl":"https://doi.org/10.1080/03461238.2022.2026459","url":null,"abstract":"This paper first studies the optimal reinsurance problems for two competitive insurers and then studies the optimal reinsurance premium pricing problem for their common reinsurer by using the dynamic programming technique. The two insurers are subject to common insurance systematic risk. Each purchases proportional or excess-of-loss reinsurance for risk control. They aim to maximize the expected utilities of their relative terminal wealth. With the insurers' optimal reinsurance strategies, the reinsurer decides the reinsurance premiums for each insurer, also aiming to maximize the expected utility of her terminal wealth. Thus, the optimal reinsurance pricing problem is formulated as a Stackelberg game between two competitive insurers and a reinsurer, where the reinsurer is the leader, and the insurers are followers. Besides, all three players take model ambiguity into account. We characterize the optimal strategies for the insurers and the reinsurer and provide some numerical examples to show the impact of competition and model ambiguity on the pricing of reinsurance contracts.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"43 1","pages":"749 - 774"},"PeriodicalIF":1.8,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74965563","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}
引用次数: 2
Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link Tweedie loss和log-link下的响应与梯度增强树、glm和神经网络
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-02-15 DOI: 10.1080/03461238.2022.2037016
Donatien Hainaut, J. Trufin, M. Denuit
{"title":"Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link","authors":"Donatien Hainaut, J. Trufin, M. Denuit","doi":"10.1080/03461238.2022.2037016","DOIUrl":"https://doi.org/10.1080/03461238.2022.2037016","url":null,"abstract":"Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. To speed up calculations, boosting is often applied to gradients of the loss function, not to responses (hence the name gradient boosting). When the model is trained by minimizing Poisson deviance, this amounts to apply the least-squares principle to raw residuals. This exposes gradient boosting to the same problems that lead to replace least-squares with Poisson Generalized Linear Models (GLM) to analyze low counts (typically, the number of reported claims at policy level in personal lines). This paper shows that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each step. Numerical illustrations demonstrate similar or better performances compared to gradient boosting when trees are used as weak learners, with a higher level of transparency since responses are used instead of gradients.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"18 1","pages":"841 - 866"},"PeriodicalIF":1.8,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74659288","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}
引用次数: 5
Robust reinsurance contract with learning and ambiguity aversion 基于学习和歧义规避的稳健再保险契约
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-02-09 DOI: 10.1080/03461238.2022.2030398
Duni Hu, Hailong Wang
{"title":"Robust reinsurance contract with learning and ambiguity aversion","authors":"Duni Hu, Hailong Wang","doi":"10.1080/03461238.2022.2030398","DOIUrl":"https://doi.org/10.1080/03461238.2022.2030398","url":null,"abstract":"We investigate the robust reinsurance demand and price under learning and ambiguity aversion. In the reinsurance contract, the insurer is ambiguity neutral and believes that he is perfectly informed, and the reinsurer is a Bayesian learner and is aware that even the filtered model is the best description of the data-generating process, might not forecast the future claims correctly. The ambiguity-averse reinsurer has a preference for reinsurance contract which is robust to model misspecification. Closed-form expressions for the robust reinsurance demand and price are derived. We find that both the reinsurer's one-sided learning and ambiguity aversion influence the structures and levels of the optimal reinsurance demand and price. Moreover, if the ambiguity-averse reinsurer specifies the suboptimal reinsurance contract as an ambiguity-neutral decision-maker, it will result in significant utility loss and the utility loss increases with ambiguity aversion level and Bayesian volatility.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"64 1","pages":"794 - 815"},"PeriodicalIF":1.8,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76261569","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}
引用次数: 3
Pareto-optimal insurance under heterogeneous beliefs and incentive compatibility 异质信念与激励相容下的帕累托最优保险
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-02-02 DOI: 10.1080/03461238.2022.2028185
Wenjun Jiang
{"title":"Pareto-optimal insurance under heterogeneous beliefs and incentive compatibility","authors":"Wenjun Jiang","doi":"10.1080/03461238.2022.2028185","DOIUrl":"https://doi.org/10.1080/03461238.2022.2028185","url":null,"abstract":"This paper studies the design of Pareto-optimal insurance under the heterogeneous beliefs of the insured and insurer. To accommodate a wide range of belief heterogeneity, we allow the likelihood ratio function to be non-monotone. To prevent the ex post moral hazard issue, the incentive compatibility condition is exogenously imposed to restrict the indemnity function. An implicit characterization of the optimal indemnity function is presented first by using the calculus of variations. Based on the point-wise maximizer to the problem, we partition the domain of loss into disjoint pieces and derive the parametric form of the optimal indemnity function over each piece through its implicit characterization. The main result of this paper generalizes those in the literature and provides insights for related problems.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"2 1","pages":"775 - 793"},"PeriodicalIF":1.8,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72877927","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}
引用次数: 0
Gambler's ruin problem in a Markov-modulated jump-diffusion risk model 马尔可夫调制跳跃-扩散风险模型中的赌徒破产问题
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-01-24 DOI: 10.1080/03461238.2021.2025145
Yuxuan Liu, Zhengjun Jiang, Yixin Qu
{"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":"8 1","pages":"682 - 694"},"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}
引用次数: 0
Modelling mortality by continuous benefit amount 通过持续受益量对死亡率进行建模
IF 1.8 3区 经济学
Scandinavian Actuarial Journal Pub Date : 2022-01-24 DOI: 10.1080/03461238.2022.2025891
S. Richards
{"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":"13 1","pages":"695 - 717"},"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}
引用次数: 2
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