Insurance Mathematics & Economics最新文献

{"title":"Optimal payout strategies when Bruno de Finetti meets model uncertainty","authors":"Yang Feng ,&nbsp;Tak Kuen Siu ,&nbsp;Jinxia Zhu","doi":"10.1016/j.insmatheco.2024.02.002","DOIUrl":"10.1016/j.insmatheco.2024.02.002","url":null,"abstract":"<div><p>Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early attempts, this paper studies the optimal payout control problem under the classical risk model taking into account of model uncertainty about the claims arrival intensity. We aim to provide insights into understanding optimal decisions incorporating model uncertainty and to examine key impact of model uncertainty. We find that the optimal strategy robust to model uncertainty is of a band type. However, the presence of the model uncertainty alters the qualitative behavior of the optimal strategy in the sense that the optimal robust policy is no longer a barrier strategy for some particular cases. We provide numerical examples to illustrate the theoretical results and examine the impact of model uncertainty on optimal payout policies. We also provide examples that use real insurance data for calibration. We discover that the decision maker takes more conservative strategies under model uncertainty, which is consistent with the findings in the economic field and has not been addressed in the existing optimal payout problems without model uncertainty.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 148-164"},"PeriodicalIF":1.9,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139919670","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":"Can price collars increase insurance loss coverage?","authors":"Indradeb Chatterjee,&nbsp;MingJie Hao,&nbsp;Pradip Tapadar,&nbsp;R. Guy Thomas","doi":"10.1016/j.insmatheco.2024.02.003","DOIUrl":"10.1016/j.insmatheco.2024.02.003","url":null,"abstract":"<div><p>Loss coverage, defined as expected population losses compensated by insurance, is a public policy criterion for comparing different risk-classification regimes. Using a model with two risk-groups (high and low) and iso-elastic demand, we compare loss coverage under three alternative regulatory regimes: (i) full risk-classification (ii) pooling (iii) a price collar, whereby each insurer is permitted to set any premiums, subject to a maximum ratio of its highest and lowest prices for different risks. Outcomes depend on the comparative demand elasticities of low and high risks. If low-risk elasticity is sufficiently low compared with high-risk elasticity, pooling is optimal; and if it is sufficiently high, full risk-classification is optimal. For an intermediate region where the elasticities are not too far apart, a price collar is optimal, but only if both elasticities are greater than one. We give extensions of these results for more than two risk-groups. We also outline how they can be applied to other demand functions using the construct of arc elasticity.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 74-94"},"PeriodicalIF":1.9,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000210/pdfft?md5=9438a824cea75585126d2e34bbb740b2&pid=1-s2.0-S0167668724000210-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139813557","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":"Inter-order relations between equivalence for Lp-quantiles of the Student's t distribution","authors":"Valeria Bignozzi ,&nbsp;Luca Merlo ,&nbsp;Lea Petrella","doi":"10.1016/j.insmatheco.2024.02.001","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.02.001","url":null,"abstract":"<div><p>In the statistical and actuarial literature, <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-quantiles, <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></math></span>, represent an important class of risk measures defined through an asymmetric <em>p</em>-power loss function that generalize the classical (<span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-)quantiles. By exploiting inter-order relations between partial moments, we show that for a Student's <em>t</em> distribution with <span><math><mi>ν</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></math></span> degrees of freedom the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ν</mi><mo>−</mo><mi>j</mi></mrow></msub></math></span>-quantile and the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span>-quantile always coincide for any <span><math><mi>j</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>ν</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span>. For instance, for a Student's <em>t</em> distribution with 4 degrees of freedom, the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-quantile and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-quantile are equal and the same holds for the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>-quantile and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-quantile; for this distribution, closed form expressions for the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-quantile, <span><math><mi>p</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span> are provided. Explicit formulas for the central moments are also established. The usefulness of exact formulas is illustrated on real-world financial data.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 44-50"},"PeriodicalIF":1.9,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139743426","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":"Random distortion risk measures","authors":"Xin Zang ,&nbsp;Fan Jiang ,&nbsp;Chenxi Xia ,&nbsp;Jingping Yang","doi":"10.1016/j.insmatheco.2024.01.008","DOIUrl":"10.1016/j.insmatheco.2024.01.008","url":null,"abstract":"<div><p>This paper presents one type of random risk measures, named as the random distortion risk measure. The random distortion risk measure is a generalization of the traditional deterministic distortion risk measure by randomizing the deterministic distortion function and the risk distribution respectively, where a stochastic distortion is introduced to randomize the distortion function, and a sub-<em>σ</em>-algebra is introduced to illustrate the influence of the known information on the risk distribution. Some theoretical properties of the random distortion risk measure are provided, such as normalization, conditional positive homogeneity, conditional comonotonic additivity, monotonicity in stochastic dominance order, and continuity from below, and a method for specifying the stochastic distortion and the sub-<em>σ</em>-algebra is provided. Based on some stochastic axioms, a representation theorem of the random distortion risk measure is proved. For considering the randomization of a given deterministic distortion risk measure, some families of random distortion risk measures are introduced with the stochastic distortions constructed from a Poisson process, a Brownian motion, and a Dirichlet process, respectively. A numerical analysis is carried out for showing the influence of the stochastic distortion and the sub-<em>σ</em>-algebra by focusing on the sample statistics, empirical distributions, and tail behavior of the random distortion risk measures.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 51-73"},"PeriodicalIF":1.9,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139825149","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":"Scenario selection with LASSO regression for the valuation of variable annuity portfolios","authors":"Hang Nguyen,&nbsp;Michael Sherris,&nbsp;Andrés M. Villegas,&nbsp;Jonathan Ziveyi","doi":"10.1016/j.insmatheco.2024.01.006","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.01.006","url":null,"abstract":"<div><p>Variable annuities (VAs) are increasingly becoming popular insurance products in many developed countries which provide guaranteed forms of income depending on the performance of the equity market. Insurance companies often hold large VA portfolios and the associated valuation of such portfolios for hedging purposes is a very time-consuming task. There have been several studies focusing on inventing techniques aimed at reducing the computational time including the selection of representative VA contracts and the use of a metamodel to estimate the values of all contracts in the portfolio. In addition to the selection of representative contracts, this paper proposes using LASSO regression to select a set of representative scenarios, which in turn allows for the set of representative contracts to expand without significant increase in computational load. The proposed approach leads to a remarkable improvement in the computational efficiency and accuracy of the metamodel.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 27-43"},"PeriodicalIF":1.9,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000179/pdfft?md5=01c3cdbbd79135e52c8f660663a5fa1f&pid=1-s2.0-S0167668724000179-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139719221","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":"A Hawkes model with CARMA(p,q) intensity","authors":"Lorenzo Mercuri ,&nbsp;Andrea Perchiazzo ,&nbsp;Edit Rroji","doi":"10.1016/j.insmatheco.2024.01.007","DOIUrl":"10.1016/j.insmatheco.2024.01.007","url":null,"abstract":"<div><p>In this paper we introduce a new model, named CARMA(p,q)-Hawkes, as the Hawkes model with exponential kernel implies a strictly decreasing behavior of the autocorrelation function while empirical evidences reject its monotonicity. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process. We also study the conditions for the stationarity and the positivity of the intensity and the strong mixing property for the increments. Furthermore, we present two estimation case studies based respectively on the likelihood and on the autocorrelation function.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 1-26"},"PeriodicalIF":1.9,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000180/pdfft?md5=13899b5c4e8b5b4f09902eb00647b5ed&pid=1-s2.0-S0167668724000180-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139679494","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":"Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models","authors":"Zhenzhen Huang ,&nbsp;Yue Kuen Kwok ,&nbsp;Ziqing Xu","doi":"10.1016/j.insmatheco.2024.01.005","DOIUrl":"10.1016/j.insmatheco.2024.01.005","url":null,"abstract":"<div><p><span><span>This paper innovates in the risk management of insurance and banking capital by exploring efficient, accurate, and reliable algorithms for evaluating risk measures and contributions in copula credit risk models. We propose a hybrid </span>saddlepoint approximation<span> algorithm, which leverages a synergy of nice analytical tractability from the saddlepoint approximation framework and efficient numerical integration from the Monte Carlo simulation<span>. Notably, the numerical integration over the systematic risk factors is enhanced using three novel numerical techniques, namely, the </span></span></span>mean shift<span> technique, randomized quasi-Monte Carlo simulation, and scalar-proxied interpolation technique. We also enhance the exponential twisting and cross entropy algorithms via the use of interpolation and update rules of optimal parameters, respectively. Extensive numerical tests on computing risk measures and risk contributions were performed on various copula models with multiple risk factors. Our hybrid saddlepoint approximation method coupled with various enhanced numerical techniques is seen to exhibit a high level of efficiency, accuracy, and reliability when compared with existing importance sampling algorithms.</span></p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"115 ","pages":"Pages 132-150"},"PeriodicalIF":1.9,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139581586","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":"Pricing guaranteed annuity options in a linear-rational Wishart mortality model","authors":"José Da Fonseca","doi":"10.1016/j.insmatheco.2024.01.004","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.01.004","url":null,"abstract":"<div><p>This paper proposes a new model, the linear-rational Wishart model, which allows the joint modelling of mortality and interest rate risks. Within this framework, we obtain closed-form solutions for the survival bond and the survival floating rate bond. We also derive a closed-form solution for the guaranteed annuity option, i.e., an option on a sum of survival (floating rate) bonds, which can be computed explicitly up to a one-dimensional numerical integration, independent of the model dimension. Using realistic parameter values, we provide a model implementation for these complex derivatives that illustrates the flexibility and efficiency of the linear-rational Wishart model.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"115 ","pages":"Pages 122-131"},"PeriodicalIF":1.9,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000106/pdfft?md5=5ea8dbcd42ba53e456e93237db33f288&pid=1-s2.0-S0167668724000106-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139548768","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":"Bootstrap consistency for the Mack bootstrap","authors":"Julia Steinmetz,&nbsp;Carsten Jentsch","doi":"10.1016/j.insmatheco.2024.01.001","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.01.001","url":null,"abstract":"<div><p>Mack's distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. Proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution of the reserve. For this purpose, Mack's model is usually equipped with a tailor-made bootstrap procedure. Although widely used in practice to estimate the reserve risk, no theoretical bootstrap consistency results exist that justify this approach.</p><p>To fill this gap in the literature, we adopt the framework proposed by <span>Steinmetz and Jentsch (2022)</span> to derive asymptotic theory in Mack's model. By splitting the reserve into two parts corresponding to process and estimation uncertainty, this enables - for the first time - a rigorous investigation also of the validity of the Mack bootstrap. We prove that the (conditional) distribution of the asymptotically dominating process uncertainty part is correctly mimicked by Mack's bootstrap if the parametric family of distributions of the individual development factors is correctly specified. Otherwise, this is not the case. In contrast, the (conditional) distribution of the estimation uncertainty part is generally not correctly captured by Mack's bootstrap. To tackle this, we propose an alternative Mack-type bootstrap, which is designed to capture also the distribution of the estimation uncertainty part.</p><p>We illustrate our findings by simulations and show that the newly proposed alternative Mack bootstrap performs superior to the Mack bootstrap.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"115 ","pages":"Pages 83-121"},"PeriodicalIF":1.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000015/pdfft?md5=e2632068fb5d1d788be9187b10f3152b&pid=1-s2.0-S0167668724000015-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139493477","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":"Moral hazard in loss reduction and state-dependent utility","authors":"S. Hun Seog ,&nbsp;Jimin Hong","doi":"10.1016/j.insmatheco.2024.01.003","DOIUrl":"10.1016/j.insmatheco.2024.01.003","url":null,"abstract":"<div><p>We consider a state-dependent utility model with a binary loss distribution, wherein moral hazard occurs in loss reduction. The findings are as follows: First, partial insurance is optimal under state-dependent utility. Second, the optimal insurance coverage and effort level are affected by the relative sizes of the marginal utilities in the loss and no-loss states. (i) If the marginal utilities are equal between the two states, the optimal coverage and effort are identical to those in the state-independent case. (ii) If the marginal utility in the loss state is greater (less) than that in the no-loss state, the optimal coverage and effort cannot simultaneously be less (greater) than those in the state-independent case. Both coverage and effort can be greater (less) than those in the state-independent case when state dependency is sufficiently large. The compensating variation decreases (increases) as state dependency increases if state dependency is sufficiently large. Although the effect of state dependency on the sensitivity of effort with respect to coverage is unclear, sensitivity decreases (increases) when the loss distribution function is convex in effort.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"115 ","pages":"Pages 151-168"},"PeriodicalIF":1.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515182","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}