Scandinavian Actuarial Journal最新文献

{"title":"Cramér–Lundberg asymptotics for spectrally positive Markov additive processes","authors":"Lucas van Kreveld, Michel Mandjes, Jan-Pieter Dorsman","doi":"10.1080/03461238.2023.2280287","DOIUrl":"https://doi.org/10.1080/03461238.2023.2280287","url":null,"abstract":"This paper studies the Cramér–Lundberg asymptotics of the ruin probability for a model in which the reserve level process is described by a spectrally-positive light-tailed Markov additive process....","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"34 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528650","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}

{"title":"Valuing equity-linked annuities under high-water mark fee structure","authors":"Kaixin Yan, Shuanming Li, Aili Zhang","doi":"10.1080/03461238.2023.2275276","DOIUrl":"https://doi.org/10.1080/03461238.2023.2275276","url":null,"abstract":"AbstractThis paper studies the valuation of equity-linked investment products embedded with a high-water mark (HWM) fee structure. Under the HWM fee structure, the insurance company charges threshold fees at a constant rate from the policyholder's account whenever the account value is lower than a pre-specified level, and levies HMW fees at another constant rate whenever the account is hitting new record highs that are higher than another pre-specified level. The dynamics of the logarithmic value of the policyholder's account, before fees, is assumed to follow either a two-sided jump-diffusion process with double exponential jumps, or a down-ward jump-diffusion process with exponential jumps. For the two-sided jump-diffusion model with HWM fees, using the Wiener–Hopf factorisation theorem and the duality lemma, we derive an explicit expression for its potential measure. For the down-ward jump-diffusion model with both threshold fees and HWM fees, we are facilitated with the excursion theory to derive an explicit expression of the potential measure. Using the above newly derived potential measures, we are able to obtain formulas for valuing the equity-linked annuity under the HWM fee structure. Finally, we illustrate our results with some numerical examples.KEYWORDS: Equity-linked annuityhigh-water mark fee structurejump-diffusion process AcknowledgementsThe authors are grateful to the anonymous referee(s) for providing valuable comments and suggestions on the earlier version of this paper which significantly improved the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is partially supported by the Fundamental Research Funds for the Central Universities (grant number 20720220044) and the National Natural Science Foundation of China (Nos. 12171405; 11661074).","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"134 14","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352101","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}

{"title":"Optimal mix among PAYGO, EET and individual savings","authors":"Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song","doi":"10.1080/03461238.2023.2274096","DOIUrl":"https://doi.org/10.1080/03461238.2023.2274096","url":null,"abstract":"AbstractIn order to deal with the aging problem, the pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different countries. In this paper, we establish the optimal mix by solving a Nash equilibrium between the pension participants and the government. Given the obligatory PAYGO and EET contribution rates, the participants choose the optimal asset allocation of the individual savings and the consumption policies to achieve the objective. The results extend the ‘Samuelson-Aaron’ criterion to age-dependent preference orderings. Under the baseline model, we identify three critical ages to distinguish the multiple outcomes of preference orderings based on heterogeneous characteristic parameters. The government is fully aware of the optimal feedback of the participants. It chooses the optimal PAYGO and EET contribution rates to maximize the overall utility of the participants weighted by each cohort's population. As such, the negative population growth rate leads to the decline of the PAYGO attractiveness as well as the increase of the older cohorts' weight in the government's decision-making. The optimal mix is the comprehensive result of the two effects.Keywords: Optimal mixPAYGO pensionEET pensionNash equilibriumshrinking population2010 Mathematics Subject Classifications: 91G0591B05JEL CLASSIFICATIONS: G22C61D81 AcknowledgmentsThe authors are particularly grateful to the two anonymous referees and the editor whose suggestions greatly improve the manuscript's quality. The authors also thank the members of the group of Actuarial Sciences and Mathematical Finance at the Department of Mathematical Sciences, Tsinghua University for their feedbacks and useful conversations.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors acknowledge the support from the National Natural Science Foundation of China [grant numbers 12271290, 11871036].","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"77 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135928317","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}

{"title":"Two hybrid models for dependent death times of couple: a common shock approach","authors":"Zied Chaieb, Domenico De Giovanni, Djibril Gueye","doi":"10.1080/03461238.2023.2264555","DOIUrl":"https://doi.org/10.1080/03461238.2023.2264555","url":null,"abstract":"AbstractWe combine two recent credit risk models with the Marshall–Olkin setup to capture the dependence structure of bivariate survival functions. The main advantage of this approach is to handle fatal shock events in the dependence structure since these two credit risk models allow one to match the time of death of an individual with a catastrophe time event. We also provide a methodology for adding other sources of dependency to our approach. In such a setup, we derive the no-arbitrage prices of some common life insurance products for coupled lives. We demonstrate the performance of our method by investigating Sibuya's dependence function. Calibration is done on the data of joint life contracts from a Canadian company.Keywords: Intensity-based modelsdependence structurefatal shock eventsjoint life insurance AcknowledgmentsThis paper has benefited from the valuable comments of one anonymous reviewer, whom the authors wish to thank. The remaining errors are the authors' only responsibility.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Throughout the paper x and y denote the ages of the husband and wife, respectively.2 Here, we have considered the independent case just for simplicity, but we could also consider, in the same spirit, the dependent case for the joint survival function using a copula function.3 In our setup, we have P(τx>s|Ft)=E[e−Γsx|FtW]E[e−Ks|FtK]. Analogous calculations can be done for the marginal probability P(τy>s|Ft).4 The authors wish to thank the Society of Actuaries, through the courtesy of Edward (Jed) Frees and Emiliano A. Valdez, for making available the data in this paper.5 This functional form of the marginal survival probability comes from assuming a stochastic intensity of the form dμh(u)=ahμh(u)+σhμh(h)dWh(u), with a,σ>0. A sufficient condition for Sh(u;t) to be a valid survival function is σ2<2dc. Additional details about this model can be found in Luciano et al. (Citation2008), Luciano & Vigna (Citation2005).6 Luciano et al. (Citation2008) refers to this model of association as the 4.2.20 Nelsen copula function. Originally proposed in Nelsen (Citation2007), a detailed study can be found in Spreeuw (Citation2006). The choice of this particular model of association is because it produces the best fit in a range of several Archimedean copulas for the data used in this paper (Luciano et al. Citation2008).Additional informationFundingDomenico De Giovanni gratefully acknowledges financial support from the PNRR project ‘Italian Ageing, Age-It’ (PE0000015 - CUP H73C22000900006) and Ministry of University and Research of Italy.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294864","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}

{"title":"Optimal reinsurance design under solvency constraints","authors":"Benjamin Avanzi, Hayden Lau, Mogens Steffensen","doi":"10.1080/03461238.2023.2257405","DOIUrl":"https://doi.org/10.1080/03461238.2023.2257405","url":null,"abstract":"We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the P and Q measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350645","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}

{"title":"Boosting cost-complexity pruned trees on Tweedie responses: the ABT machine for insurance ratemaking","authors":"Julie Huyghe, Julien Trufin, Michel Denuit","doi":"10.1080/03461238.2023.2258135","DOIUrl":"https://doi.org/10.1080/03461238.2023.2258135","url":null,"abstract":"AbstractThis paper proposes a new boosting machine based on forward stagewise additive modeling with cost-complexity pruned trees. In the Tweedie case, it deals directly with observed responses, not gradients of the loss function. Trees included in the score progressively reduce to the root-node one, in an adaptive way. The proposed Adaptive Boosting Tree (ABT) machine thus automatically stops at that time, avoiding to resort to the time-consuming cross validation approach. Case studies performed on motor third-party liability insurance claim data demonstrate the performances of the proposed ABT machine for ratemaking, in comparison with regular gradient boosting trees.Keywords: Risk classificationboostinggradient boostingregression treescost-complexity pruning Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135149922","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}

{"title":"Ruin in a continuous-time risk model with arbitrarily dependent insurance and financial risks triggered by systematic factors","authors":"Yang Yang, Yahui Fan, Kam Chuen Yuen","doi":"10.1080/03461238.2023.2256508","DOIUrl":"https://doi.org/10.1080/03461238.2023.2256508","url":null,"abstract":"AbstractThis paper is devoted to asymptotic analysis for a continuous-time risk model with the insurance surplus process and the log-price process of the investment driven by two dependent jump-diffusion processes. We take into account arbitrary dependence between the insurance claims and their corresponding investment return jumps caused by a sequence of systematic factors, whose arrival times constitute a renewal counting process. Under the framework of regular variation, we obtain a simple and unified asymptotic formula for the finite-time ruin probability as the initial wealth becomes large. It turns out that, in the weakly dependent case, the tails of the claims determine the exact decay rate of the finite-time ruin probability while the investment return jumps only contribute to the coefficient of the asymptotic formula; however, in the strongly dependent case, they both produce essential impacts on the finite-time ruin probability which is under-estimated in the weakly dependent case.Keywords: Asymptoticsfinite-time ruin probabilitysystematic factorsinsurance claimsinvestment return jumpsMSC: 62P0562E1091B30 AcknowledgmentsThe authors would like to thank the anonymous referee for his/her suggestive comments and very careful reading of the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 According to the American Council of Life Insurers, ‘life insurers are a major source of bond financing for American business, holding more than 22% of all U.S. corporate bonds’ and ‘life insurers provide long-term capital to the commercial mortgage market, financing more than 515 billion dollars, or almost one-sixth, of U.S. commercial mortgages’. The Annual Report 2021 of Allianz Group stated that as of 31 December 2021, the overall asset portfolio has reached 808.5 billion euros mainly in the debt investments (672.3 billion decreased by 10.1 billion compared to year end 2020, mainly due to market movements), about 91% of which was invested in investment-grade bonds and loans. See page 90. Available at https://www.allianz.com/en/investorrelations/results-reports/annual-reports.2 See a report from the International Monetary Fund (2016). The insurance sector: trends and systemic risks implications. Available at https://www.imf.org/External/Pubs/FT/GFSR/2016/01/pdf/c3.pdf.3 The collapse and near-failure of the insurance giant American International Group was caused largely by its 526 billion dollars portfolio of credit default swaps.4 The American Property Casualty Insurance Association estimated that the monthly COVID-19 business interruption losses just for businesses with 100 or fewer employees was 255–431 billion dollars per month. Available at http://www.pciaa.net/pciwebsite/cms/content/viewpage?sitePageId=60052.5 The business segment Asset Management of the Allianz Group was impacted by the severe financial market disruption and related investor uncertainties which led to a negative market valuation of as","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784501","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}

{"title":"A stochastic model of group wealth responses to insurance mechanisms in low-income communities","authors":"Kira Henshaw, Michel Mandjes, Corina Constantinescu","doi":"10.1080/03461238.2023.2251197","DOIUrl":"https://doi.org/10.1080/03461238.2023.2251197","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135879236","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}

{"title":"Stackelberg reinsurance chain under model ambiguity","authors":"Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou","doi":"10.1080/03461238.2023.2255399","DOIUrl":"https://doi.org/10.1080/03461238.2023.2255399","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"6 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78516253","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}

{"title":"Isotonic recalibration under a low signal-to-noise ratio","authors":"Mario V. Wüthrich, Johanna Ziegel","doi":"10.1080/03461238.2023.2246743","DOIUrl":"https://doi.org/10.1080/03461238.2023.2246743","url":null,"abstract":"Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to restore auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to an explainable pricing system because the resulting isotonically recalibrated regression function has a low complexity.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136337408","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}