{"title":"Robust parameter estimation for the Lee-Carter family: A probabilistic principal component approach","authors":"Yiping Guo , Johnny Siu-Hang Li","doi":"10.1016/j.insmatheco.2025.103164","DOIUrl":"10.1016/j.insmatheco.2025.103164","url":null,"abstract":"<div><div>Although the impact of outliers on stochastic mortality modelling has been examined, previous studies on this topic focus on how outliers in the estimated time-varying indexes may be detected and/or modelled, with little attention being paid to the adverse effects of outliers on estimation robustness, particularly that pertaining to age-specific parameters. In this paper, we propose a robust estimation method for the Lee-Carter model, through a reformulation of the model into a probabilistic principal component analysis with multivariate <em>t</em>-distributions and an efficient expectation-maximization algorithm for implementation. The proposed method yields significantly more robust parameter estimates, while preserving the fundamental interpretation for the bilinear term in the model as the first principal component and the flexibility of pairing the estimated time-varying parameters with any appropriate time-series process. We also extend the proposed method for use with multi-population generalizations of the Lee-Carter model, allowing for a wider range of applications such as quantification of population basis risk in index-based longevity hedges. Using a combination of real and pseudo datasets, we demonstrate the superiority of the proposed method relative to conventional estimation approaches such as singular value decomposition and maximum likelihood.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103164"},"PeriodicalIF":2.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145265697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Individual survivor fund account: The impact of bequest motives on tontine participation","authors":"Tak Wa Ng, Thai Nguyen","doi":"10.1016/j.insmatheco.2025.103161","DOIUrl":"10.1016/j.insmatheco.2025.103161","url":null,"abstract":"<div><div>We introduce a new model for individual survivor fund account with bequest that allows the tontine's participants to leave inheritances to their heirs. Two proposed designs, constant and variable participation, are examined through the lens of an individual account, addressing optimal investment and bequest proportions. Our formulation captures two types of bequest motives: the relative concern between terminal benefit and premature bequest and the intention to smooth the bequest plan. Our numerical illustrations show that the individual's willingness to participate in the longevity risk pool will decrease with these two bequest motive levels and address the question of when and with what motive level the individual will join the pool. Furthermore, we incorporate labor income and consumption in the participant's optimization problem and perform a welfare analysis thereon.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103161"},"PeriodicalIF":2.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic investment-driven insurance pricing and optimal regulation","authors":"Bingzheng Chen , Zongxia Liang , Shunzhi Pang","doi":"10.1016/j.insmatheco.2025.103160","DOIUrl":"10.1016/j.insmatheco.2025.103160","url":null,"abstract":"<div><div>This paper analyzes the competitive equilibrium of insurance market in a dynamic setting, focusing on the interaction between insurers' underwriting and investment strategies. Three possible equilibrium outcomes are identified: a positive insurance market, a zero insurance market, and market failure. Our findings reveal why insurers may rationally accept underwriting losses by setting a negative safety loading while relying on investment profits, particularly when there is a negative correlation between insurance gains and financial returns. Such losses can still occur even when the insurance market is monopolistic. Additionally, we explore the impact of regulatory frictions, showing that while imposing a cost on investment can enhance social welfare under certain conditions, it may not always be necessary.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103160"},"PeriodicalIF":2.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francesca Perla , Salvatore Scognamiglio , Andrea Spadaro , Paolo Zanetti
{"title":"Transformers-based least square Monte Carlo for solvency calculation in life insurance","authors":"Francesca Perla , Salvatore Scognamiglio , Andrea Spadaro , Paolo Zanetti","doi":"10.1016/j.insmatheco.2025.103163","DOIUrl":"10.1016/j.insmatheco.2025.103163","url":null,"abstract":"<div><div>The Solvency Capital Requirement (SCR), mandated by Solvency II, represents the capital insurers must hold to ensure solvency, calculated as the Value-at-Risk of the Net Asset Value at a 99.5% confidence level over a one-year period. While Nested Monte Carlo simulations are the gold standard for SCR calculation, they are highly resource-intensive. The Least Squares Monte Carlo (LSMC) method provides a more efficient alternative but faces challenges with high-dimensional data due to the curse of dimensionality. We introduce a novel extension of LSMC, incorporating advanced deep learning models, specifically Transformer models, which enhance traditional machine learning methods. This approach significantly improves the accuracy of approximating the complex relationship between insurance liabilities and risk factors, leading to a more accurate SCR calculation. Our extensive experiments on two insurance portfolios demonstrate the effectiveness of this transformer-based LSMC approach. Additionally, we show that Shapley values can be applied to achieve model explainability, which is crucial for regulatory compliance and for fostering the adoption of deep learning in the highly regulated insurance sector.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103163"},"PeriodicalIF":2.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic derivative-based pension investment with stochastic volatility: A behavioral perspective","authors":"Zheng Chen , Zhongfei Li , Yan Zeng , Yang Shen","doi":"10.1016/j.insmatheco.2025.103158","DOIUrl":"10.1016/j.insmatheco.2025.103158","url":null,"abstract":"<div><div>We study a derivative-based optimal investment strategy for a defined contribution (DC) pension plan under the Heston stochastic volatility model. The investor's preferences are described by an S-shaped utility that combines risk-seeking and loss-averse behaviors, benchmarked to a reference point of retirement savings. By the martingale approach and the inverse Fourier transform method, we obtain a semi-analytical form for the optimal investment strategy. We investigate the distinct roles of various factors, such as preferences, wealth goals, market conditions, in the investor's optimal decision, and clarify the dynamic relationship between these factors and derivatives trading. We also provide comprehensive comparisons between the results derived under prospect theory and expected utility theory. A portfolio decomposition validates that the optimal derivatives trading strategy is influenced by both psychological and risk-averse factors. Numerical illustrations are provided to further elaborate our results.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103158"},"PeriodicalIF":2.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust time-consistent Stackelberg differential game for insurance with stochastic interest rates and 4/2 stochastic volatility","authors":"Hao Chang, Xiao-Jia Li","doi":"10.1016/j.insmatheco.2025.103159","DOIUrl":"10.1016/j.insmatheco.2025.103159","url":null,"abstract":"<div><div>This paper studies the robust time-consistent investment-reinsurance problem for an insurer and a reinsurer under the framework of the Stackelberg stochastic differential game, in which the reinsurer is the leader and the insurer is the follower. The insurer hedges the claim risk by purchasing proportional reinsurance, and both the insurer and reinsurer can invest in a financial market consisting of a risk-free asset, a stock, and a rolling bond to manage risk. The interest rates and the volatility of stock price are assumed to obey the affine term-structure model and the 4/2 stochastic volatility model, respectively. Assume that both the insurer and the reinsurer are ambiguity-averse, and we establish the robust optimal control problem for an insurer and a reinsurer under the mean-variance criterion, respectively. Robust time-consistent investment and reinsurance strategies are determined by the Stackelberg equilibrium of the game, which considers the interests of both the insurer and the reinsurer and reflects the information asymmetry between the two parties. By employing the stochastic optimal control theory, we derive the robust time-consistent Stackelberg strategies. Finally, some sensitivity analysis and comparative analysis are presented to illustrate the results obtained.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103159"},"PeriodicalIF":2.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Censored and extreme losses: Functional convergence and applications to tail goodness-of-fit","authors":"Martin Bladt, Christoffer Øhlenschlæger","doi":"10.1016/j.insmatheco.2025.103157","DOIUrl":"10.1016/j.insmatheco.2025.103157","url":null,"abstract":"<div><div>This paper establishes the functional convergence of the Extreme Nelson–Aalen and Extreme Kaplan–Meier estimators, which are designed to capture the heavy-tailed behavior of censored losses. The resulting limit representations can be used to obtain the distributions of functionals with respect to the so-called tail process. For instance, we may recover the convergence of a censored Hill estimator, and we further investigate two goodness-of-fit statistics for the tail of the loss distribution. Using the latter limit theorems, we propose two rules for selecting a suitable number of order statistics, both based on test statistics derived from the functional convergence results. The effectiveness of these selection rules is investigated through simulations and an application to a real dataset comprised of French motor insurance claim sizes.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103157"},"PeriodicalIF":2.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Diversification effect in multivariate optimal risk transfer","authors":"Vali Asimit , Tsz Chai Fung , Liang Peng , Fang Yang","doi":"10.1016/j.insmatheco.2025.103156","DOIUrl":"10.1016/j.insmatheco.2025.103156","url":null,"abstract":"<div><div>There are two main practical questions in the context of multivariate risk transfers. First, non-intragroup risk transfers raise the question of whether to purchase (re)insurance coverage for the aggregate risk or separately for each risk. Second, intragroup risk transfers are always challenged by regulators on whether there is a commercial purpose in such transactions, and therefore, insurance buyers must commercially validate their decisions. This paper investigates the diversification effect from the buyer's and the seller's perspectives. Our analysis for insurance buyers is based on the ratio between the optimal reinsurance risk margin cost for the total sum of losses and the sum of the individual optimal risk margin costs for each loss type. Because analytical comparison is infeasible, we develop a statistical inference method for this ratio and evaluate its finite sample performance through simulation. The seller's perspective is modeled via a new measure to assess the relative profitability of offering joint versus separate risk transfer contracts. The combined use of these measures enables both buyers and sellers to identify optimal risk transfer decisions that are commercially viable for both parties. Finally, we apply the proposed inference methods to the widely studied Danish fire loss dataset, illustrating the practical implications of our findings that equally apply to an intragroup or non-intragroup risk transfer.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103156"},"PeriodicalIF":2.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Laura Iveth Aburto Barrera , Anna Nicolet , Christophe Bagnoud , Joachim Marti , Joël Wagner
{"title":"Development of multimorbidity patterns in older adults in Switzerland: A competing risks modeling approach","authors":"Laura Iveth Aburto Barrera , Anna Nicolet , Christophe Bagnoud , Joachim Marti , Joël Wagner","doi":"10.1016/j.insmatheco.2025.103155","DOIUrl":"10.1016/j.insmatheco.2025.103155","url":null,"abstract":"<div><div>Multimorbidity, multiple long-term health conditions co-occurring in one individual, is a complex challenge that affects individuals, healthcare systems, and society. People with multimorbidity have a lower quality of life, higher mortality, and more complex needs and holistic treatments, resulting in higher health insurance and overall healthcare costs. Our study aims to investigate the progression of multimorbidity by identifying the main disease patterns in the adult population. Using an extensive dataset of health insurance claims from one of the largest Swiss health insurance companies, we categorize chronic long-term diseases into different pharmacy cost groups based on a medical classification system to assess the morbidity status of insureds. Developing on a competing risks framework, we use subdistribution hazard models adjusted for age effects to model key multimorbidity patterns, considering the most prevalent chronic diseases in the population. Our analysis focuses on estimating cumulative incidence functions for gender-specific trajectories. By shedding light on these patterns, our study contributes to a deeper understanding of multimorbidity dynamics and potential patient pathways. It provides information for decision-makers, financial planners, and healthcare professionals to enable optimal resource allocation and facilitate prevention and interventions tailored to the needs of various morbidity groups to reduce the disease burden and economic impact.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103155"},"PeriodicalIF":2.2,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An optimal periodic dividend and risk control problem for an insurance company","authors":"Mark Kelbert, Harold A. Moreno-Franco","doi":"10.1016/j.insmatheco.2025.103154","DOIUrl":"10.1016/j.insmatheco.2025.103154","url":null,"abstract":"<div><div>We study the problem of optimal risk policies and dividend strategies for an insurance company operating under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poisson process. Concurrently, risk control is continuously managed through proportional reinsurance. Our analysis confirms the optimality of a periodic-classical barrier strategy for maximizing the expected net present value until the first instance of bankruptcy across all admissible periodic-classical strategies.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103154"},"PeriodicalIF":2.2,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}