{"title":"Fitting Tweedie's compound Poisson model to pure premium with the EM algorithm","authors":"Guangyuan Gao","doi":"10.1016/j.insmatheco.2023.10.002","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.10.002","url":null,"abstract":"<div><p><span>We consider the situation when the number of claims is unavailable, and a Tweedie's compound Poisson model is fitted to the observed pure premium. Currently, there are two different models based on the Tweedie distribution: a single </span>generalized linear model<span><span> (GLM) for mean and a double generalized linear model (DGLM) for both mean and dispersion. Although the DGLM approach facilitates the heterogeneous dispersion, its soundness relies on the accuracy of the saddlepoint approximation, which is poor when the proportion of zero claims is large. For both models, the power variance parameter is estimated by considering the profile likelihood, which is computationally expensive. We propose a new approach to fit the Tweedie model with the </span>EM algorithm, which is equivalent to an iteratively re-weighted Poisson-gamma model on an augmented data set. The proposed approach addresses the heterogeneous dispersion without needing the saddlepoint approximation, and the power variance parameter is estimated during the model fitting. Numerical examples show that our proposed approach is superior to the two competing models.</span></p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"114 ","pages":"Pages 29-42"},"PeriodicalIF":1.9,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138395977","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}
Anna Rita Bacinello , Rosario Maggistro , Ivan Zoccolan
{"title":"Risk-neutral valuation of GLWB riders in variable annuities","authors":"Anna Rita Bacinello , Rosario Maggistro , Ivan Zoccolan","doi":"10.1016/j.insmatheco.2023.10.001","DOIUrl":"10.1016/j.insmatheco.2023.10.001","url":null,"abstract":"<div><p><span>In this paper we propose a model for pricing GLWB variable annuities under a stochastic mortality framework. Our set-up is very general and only requires the Markovian property<span> for the mortality intensity and the asset price processes. The contract value is defined through an optimization problem which is solved by using dynamic programming. We prove, by backward induction, the validity of the bang-bang condition for the set of discrete withdrawal strategies of the model. This result is particularly remarkable as in the insurance literature either the existence of optimal bang-bang controls is assumed or it requires suitable conditions. We assume constant </span></span>interest rates, although our results still hold in the case of a Markovian interest rate process. We present extensive numerical examples, modelling the mortality intensity as a non mean reverting square root process and the asset price as an exponential Lévy process, and compare the results obtained for different parameters and policyholder behaviours.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"114 ","pages":"Pages 1-14"},"PeriodicalIF":1.9,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566322","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":"Analyzing the interest rate risk of equity-indexed annuities via scenario matrices","authors":"Sascha Günther, Peter Hieber","doi":"10.1016/j.insmatheco.2023.10.003","DOIUrl":"10.1016/j.insmatheco.2023.10.003","url":null,"abstract":"<div><p>The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. We discuss a so-called cliquet-style or ratchet-type guarantee granting a minimum annual return. Its path-dependent payoff complicates valuation and risk management, especially if interest rates are modelled stochastically. We develop a novel scenario-matrix (SM) method. In the example of a Vasicek-Black-Scholes model, we derive closed-form expressions for the value and moment-generating function of the final payoff in terms of the scenario matrix. This allows efficient evaluation of values and various risk measures, avoiding Monte-Carlo simulation or numerical Fourier inversion. In numerical tests, this procedure proves to converge quickly and outperforms the existing approaches in the literature in terms of computation time and accuracy.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"114 ","pages":"Pages 15-28"},"PeriodicalIF":1.9,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668723000884/pdfft?md5=eb62819e6a8fba972fe783e25593770a&pid=1-s2.0-S0167668723000884-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Diagnostic tests before modeling longitudinal actuarial data","authors":"Yinhuan Li , Tsz Chai Fung , Liang Peng , Linyi Qian","doi":"10.1016/j.insmatheco.2023.09.002","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.09.002","url":null,"abstract":"<div><p>In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely the serial dynamic test and correlation test, to assess the appropriateness of these assumptions and provide justifiable modeling directions. The tests involve the following ingredients: i) computing the change of the cross-sectional estimated parameters under a logistic regression model and the empirical residual correlations of the claim occurrence indicators across time, which serve as the indications to detect serial dynamics; ii) quantifying estimation uncertainty using the randomly weighted bootstrap approach; iii) developing asymptotic theories to construct proper test statistics. The proposed tests are examined by simulated data and applied to two non-life insurance datasets, revealing that the two datasets behave differently.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"113 ","pages":"Pages 310-325"},"PeriodicalIF":1.9,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49851249","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":"Optimal risk management with reinsurance and its counterparty risk hedging","authors":"Yichun Chi , Tao Hu , Yuxia Huang","doi":"10.1016/j.insmatheco.2023.09.003","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.09.003","url":null,"abstract":"<div><p>In this paper, we revisit the study of an optimal risk management strategy for an insurer who wants to maximize the expected utility by purchasing reinsurance and managing reinsurance counterparty risk with a default-free hedging instrument, where the reinsurance premium is calculated by the expected value principle and the price of the hedging instrument equals the expected payoff plus a proportional loading. Different to previous studies, we exclude ex post moral hazard by imposing the no-sabotage condition on reinsurance contracts and derive the optimal strategy analytically. We find that the stop-loss reinsurance is always optimal, but the form of the optimal hedging payoff depends on the cost difference between reinsurance and hedging instrument. We further show that full risk transfer is optimal if and only if both reinsurance pricing and the hedging price are fair. Finally, numerical analyses are conducted to illustrate the effects of some interesting factors on the optimal risk management strategy.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"113 ","pages":"Pages 274-292"},"PeriodicalIF":1.9,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49851145","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":"Two-phase selection of representative contracts for valuation of large variable annuity portfolios","authors":"Ruihong Jiang, David Saunders, Chengguo Weng","doi":"10.1016/j.insmatheco.2023.08.009","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.08.009","url":null,"abstract":"<div><p>A computationally appealing methodology for the valuation of large variable annuities portfolios is a metamodelling framework that evaluates a small set of representative contracts, fits a predictive model based on these computed values, and then extrapolates the model to estimate the values of the remaining contracts. This paper proposes a new two-phase procedure for selecting representative contracts. The representatives from the first phase are determined using contract attributes as in existing metamodelling approaches, but those in the second phase are chosen by utilizing the information contained in the values of the representatives from the first phase. Two numerical studies confirm that our two-phase selection procedure improves upon conventional approaches from the existing literature.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"113 ","pages":"Pages 293-309"},"PeriodicalIF":1.9,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49851131","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 optimal asset-liability management with mispricing and stochastic factor market dynamics","authors":"Ning Wang , Yumo Zhang","doi":"10.1016/j.insmatheco.2023.09.001","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.09.001","url":null,"abstract":"<div><p>This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"113 ","pages":"Pages 251-273"},"PeriodicalIF":1.9,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49851144","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":"European option pricing with market frictions, regime switches and model uncertainty","authors":"Tak Kuen Siu","doi":"10.1016/j.insmatheco.2023.08.008","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.08.008","url":null,"abstract":"<div><p>The impact of market frictional costs on pricing insurance and financial products in a regime-switching environment has not been well-explored. This paper introduces a general pricing model for European options which incorporates market frictional costs, regime switches and model uncertainty. Regime switches are due to changes in an economic environment. Model uncertainty is attributed to misspecification of transition intensities for economic regimes. The selling and buying prices of a European option are determined through stochastic optimal control and nonlinear partial differential equations. A fair value is determined by a closed-form solution to a minimization problem based on a relative entropy. The fair value is consistent with the one obtained using the Esscher transform, which is an important tool in actuarial science. Numerical methods and results for implementing the pricing model are presented. The results indicate that after controlling for the model uncertainty, market frictional costs are more significant than regime switches in accounting for the fair, selling and buying prices.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"113 ","pages":"Pages 233-250"},"PeriodicalIF":1.9,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49851146","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":"Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin","authors":"Xiaoqing Liang , Virginia R. Young","doi":"10.1016/j.insmatheco.2023.06.003","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2023.06.003","url":null,"abstract":"<div><p>We minimize the probability of lifetime ruin in a deterministic financial and insurance model, although the investor's time of death is random, with an age-dependent force of mortality. By contrast with the traditional anything-anytime annuitization model (that is, individuals can annuitize any fraction of their wealth at anytime), the individual only purchases life annuity income gradually, using a bounded, absolutely continuous rate. As in the anything-anytime annuitization case, we find that it is optimal for the individual not to purchase additional annuity income when her wealth is less than a specific linear function of her existing annuity income, which we call the <em>buy boundary</em>. Interestingly, we find the buy boundary in our model is identical to the one in the anything-anytime annuitization model. However, there is a separate threshold, which we call the <em>safe level</em>. (This threshold degenerates to the buy boundary in the anything-anytime annuitization model.) When wealth is greater than the safe level, the minimum probability of lifetime ruin is zero; when wealth lies between the buy boundary and the safe level, the individual's best choice is to purchase annuity income at the maximum allowable rate.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"112 ","pages":"Pages 80-96"},"PeriodicalIF":1.9,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49838188","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}