Pub Date : 2022-11-07DOI: 10.1080/03461238.2022.2139631
Xue Dong, X. Rong, H Zhao
ABSTRACT This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, where we adopt the different classes of premium principles (including the expected value premium principle, the variance premium principle and the exponential premium principle) and each insurer aims to maximize the expected exponential utility of his terminal wealth relative to that of his competitor. Moreover, both insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks and can invest in a financial market consisting of a risk-free asset, a risky asset where the instantaneous rate of investment return follows an Ornstein-Uhlenbeck process which can reflect the changes of bull market and bear market. The optimal reinsurance strategy has a non-trivial structure which is distinguished from the conventional proportional and excess-of-loss reinsurance strategies. Furthermore, we derive the optimal reinsurance and investment strategies under the variance premium principle and expected value principle. In addition, we give another model which considers the correlation between risk model and financial market under the expected value principle. Finally, numerical analyses are provided to analyze the effects of model parameters on the optimal strategies under different cases.
{"title":"Non-zero-sum reinsurance and investment game with non-trivial curved strategy structure under Ornstein–Uhlenbeck process","authors":"Xue Dong, X. Rong, H Zhao","doi":"10.1080/03461238.2022.2139631","DOIUrl":"https://doi.org/10.1080/03461238.2022.2139631","url":null,"abstract":"ABSTRACT This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, where we adopt the different classes of premium principles (including the expected value premium principle, the variance premium principle and the exponential premium principle) and each insurer aims to maximize the expected exponential utility of his terminal wealth relative to that of his competitor. Moreover, both insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks and can invest in a financial market consisting of a risk-free asset, a risky asset where the instantaneous rate of investment return follows an Ornstein-Uhlenbeck process which can reflect the changes of bull market and bear market. The optimal reinsurance strategy has a non-trivial structure which is distinguished from the conventional proportional and excess-of-loss reinsurance strategies. Furthermore, we derive the optimal reinsurance and investment strategies under the variance premium principle and expected value principle. In addition, we give another model which considers the correlation between risk model and financial market under the expected value principle. Finally, numerical analyses are provided to analyze the effects of model parameters on the optimal strategies under different cases.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88100751","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}
Pub Date : 2022-11-07DOI: 10.1080/03461238.2022.2142157
Jingyi Cao, V. Young
The classical Cramér–Lundberg risk process is commonly used to model the surplus of an insurer; it characterizes the claim arrival process and the claim size random variable Y through a compound Poisson process, along with a constant rate of premium income. When , the process can be approximated by a diffusion process, but that requirement eliminates many heavy-tailed claim models, such as the Pareto with . In this paper, we generalize the well known diffusion approximation by assuming that Y lies in the domain of attraction of an α-stable random variable, for . Then, we construct a sequence of classical Cramér–Lundberg risk processes and show that the sequence converges to an α-stable Lévy motion in the Skorokhod -topology. We prove this convergence by proving the pointwise convergence of the corresponding Laplace exponents of our processes, which to our knowledge, is a new result. To apply this convergence result, we show the convergence of a sequence of Gerber–Shiu distributions of exponential Parisian ruin, and we show the convergence of a sequence of payoff functions for barrier dividend strategies. Both of these applications provide new proofs of the stated limits.
{"title":"Approximating the classical risk process by stable Lévy motion","authors":"Jingyi Cao, V. Young","doi":"10.1080/03461238.2022.2142157","DOIUrl":"https://doi.org/10.1080/03461238.2022.2142157","url":null,"abstract":"The classical Cramér–Lundberg risk process is commonly used to model the surplus of an insurer; it characterizes the claim arrival process and the claim size random variable Y through a compound Poisson process, along with a constant rate of premium income. When , the process can be approximated by a diffusion process, but that requirement eliminates many heavy-tailed claim models, such as the Pareto with . In this paper, we generalize the well known diffusion approximation by assuming that Y lies in the domain of attraction of an α-stable random variable, for . Then, we construct a sequence of classical Cramér–Lundberg risk processes and show that the sequence converges to an α-stable Lévy motion in the Skorokhod -topology. We prove this convergence by proving the pointwise convergence of the corresponding Laplace exponents of our processes, which to our knowledge, is a new result. To apply this convergence result, we show the convergence of a sequence of Gerber–Shiu distributions of exponential Parisian ruin, and we show the convergence of a sequence of payoff functions for barrier dividend strategies. Both of these applications provide new proofs of the stated limits.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79472001","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}
Pub Date : 2022-11-07DOI: 10.1080/03461238.2022.2139630
C. Bernard, Corrado De Vecchi, S. Vanduffel
The assessment of portfolio risk is often explicitly (e.g. the Basel III square root formula) or implicitly (e.g. credit risk models) driven by the marginal distributions of the risky components and their correlations. We assess the extent by which such practice is prone to model error. In the case of n = 2 risks, we investigate under which conditions the unconstrained Value-at-Risk (VaR) bounds (which are the maximum and minimum VaR for when only the marginal distributions of the are known) coincide with the (constrained) VaR bounds when in addition one has information on some measure of dependence (e.g. Pearson correlation or Spearman's rho). We find that both bounds coincide if the measure of dependence takes value in an interval that we explicitly determine. For probability levels used in risk management practice, we show that using correlation information has typically no effect on the highest possible VaR whereas it can affect the lowest possible VaR. In the case of a general sum of risks, we derive Range Value-at-Risk (RVaR) bounds under an average correlation constraint and we show they are best-possible in the case of a sum of standard uniformly distributed risks.
{"title":"The impact of correlation on (Range) Value-at-Risk","authors":"C. Bernard, Corrado De Vecchi, S. Vanduffel","doi":"10.1080/03461238.2022.2139630","DOIUrl":"https://doi.org/10.1080/03461238.2022.2139630","url":null,"abstract":"The assessment of portfolio risk is often explicitly (e.g. the Basel III square root formula) or implicitly (e.g. credit risk models) driven by the marginal distributions of the risky components and their correlations. We assess the extent by which such practice is prone to model error. In the case of n = 2 risks, we investigate under which conditions the unconstrained Value-at-Risk (VaR) bounds (which are the maximum and minimum VaR for when only the marginal distributions of the are known) coincide with the (constrained) VaR bounds when in addition one has information on some measure of dependence (e.g. Pearson correlation or Spearman's rho). We find that both bounds coincide if the measure of dependence takes value in an interval that we explicitly determine. For probability levels used in risk management practice, we show that using correlation information has typically no effect on the highest possible VaR whereas it can affect the lowest possible VaR. In the case of a general sum of risks, we derive Range Value-at-Risk (RVaR) bounds under an average correlation constraint and we show they are best-possible in the case of a sum of standard uniformly distributed risks.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79221989","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}
Pub Date : 2022-11-07DOI: 10.1080/03461238.2022.2141656
J. Kirkby, Jean-Philippe Aguilar
This work studies the valuation and optimal surrender of variable (equity-linked) annuities under a Lévy-driven equity market with mortality risk. We consider a practical periodic fee structure which can vary over time and is assessed as a proportion of the fund value. At maturity, the fund value is returned to the policyholder according to a guaranteed minimum accumulation benefit (GMAB). Mortality risk is also modeled discretely, and the contract offers a guaranteed minimum death benefit (GMBD) prior to maturity. The benefits accommodate caps on the growth of funds (in addition to the rising floor) to reduce the fee level and as a disincentive to early surrender. Interest rates are modeled via a deterministic discounting term structure, which can be calibrated (bootstrapped) to the rates market, according to market convention. An efficient and accurate valuation framework is developed, along with closed form pricing formulas in the case where policy surrender is not permitted. Numerous experiments are conducted to illustrate the interplay between contract parameters and the decision to surrender, and we provide an extensive analysis that investigates how to structure contracts to disincentivize early surrender.
{"title":"Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees","authors":"J. Kirkby, Jean-Philippe Aguilar","doi":"10.1080/03461238.2022.2141656","DOIUrl":"https://doi.org/10.1080/03461238.2022.2141656","url":null,"abstract":"This work studies the valuation and optimal surrender of variable (equity-linked) annuities under a Lévy-driven equity market with mortality risk. We consider a practical periodic fee structure which can vary over time and is assessed as a proportion of the fund value. At maturity, the fund value is returned to the policyholder according to a guaranteed minimum accumulation benefit (GMAB). Mortality risk is also modeled discretely, and the contract offers a guaranteed minimum death benefit (GMBD) prior to maturity. The benefits accommodate caps on the growth of funds (in addition to the rising floor) to reduce the fee level and as a disincentive to early surrender. Interest rates are modeled via a deterministic discounting term structure, which can be calibrated (bootstrapped) to the rates market, according to market convention. An efficient and accurate valuation framework is developed, along with closed form pricing formulas in the case where policy surrender is not permitted. Numerous experiments are conducted to illustrate the interplay between contract parameters and the decision to surrender, and we provide an extensive analysis that investigates how to structure contracts to disincentivize early surrender.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89728425","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}
Pub Date : 2022-10-18DOI: 10.1080/03461238.2022.2133625
Jae Youn Ahn, Himchan Jeong, Yang Lu
The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, natural disaster forecasting, as well as operational risk in banking regulation. This model, initially designed for cross-sectional data, has recently been adapted to a longitudinal context for both a priori and a posteriori ratemaking, through random effects specifications. However, the random effects are usually assumed to be static due to computational concerns, leading to predictive premiums that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effects processes. The model is based on Bayesian state-space models. It is associated with a simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. A real data application for auto insurance is proposed to show the performance of our method.
{"title":"A simple Bayesian state-space approach to the collective risk models","authors":"Jae Youn Ahn, Himchan Jeong, Yang Lu","doi":"10.1080/03461238.2022.2133625","DOIUrl":"https://doi.org/10.1080/03461238.2022.2133625","url":null,"abstract":"The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, natural disaster forecasting, as well as operational risk in banking regulation. This model, initially designed for cross-sectional data, has recently been adapted to a longitudinal context for both a priori and a posteriori ratemaking, through random effects specifications. However, the random effects are usually assumed to be static due to computational concerns, leading to predictive premiums that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effects processes. The model is based on Bayesian state-space models. It is associated with a simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. A real data application for auto insurance is proposed to show the performance of our method.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90556496","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}
Pub Date : 2022-09-14DOI: 10.1080/03461238.2022.2111529
A. Balbás, B. Balbás, Raquel Balbás, Antonio J. Heras
The objective of this paper is twofold. On the one hand, the optimal combination of reinsurance and financial investment will be studied under a general framework. Indeed, there is no specific type of reinsurance contract, there is no specific dynamics of the involved financial instruments and the financial market does not have to be free of frictions. On the other hand, it will be pointed out how the optimal combination above may provide us with new premium principles making the insurer global risk vanish. The risk will be managed with a coherent risk measure, and the new premium principles will seem to reflect several properties, which are desirable from both the analytical and the economic perspectives. From the analytical viewpoint, the premium principles will be continuous, homogeneous and increasing. From the economic viewpoint, the premium principles will lead to cheaper prices with respect to both the insurance market and the financial one. In other words, the premium principles will make the insurer more competitive in prices under a null risk. General necessary and sufficient optimality conditions will be given, as well as closed forms for the solutions under appropriate assumptions. Several methods preventing unbounded optimization problems will warrant special attention, and one particular case will be more thoroughly studied, namely, the combination of the Black–Scholes–Merton pricing model with the conditional value at risk.
{"title":"Actuarial pricing with financial methods","authors":"A. Balbás, B. Balbás, Raquel Balbás, Antonio J. Heras","doi":"10.1080/03461238.2022.2111529","DOIUrl":"https://doi.org/10.1080/03461238.2022.2111529","url":null,"abstract":"The objective of this paper is twofold. On the one hand, the optimal combination of reinsurance and financial investment will be studied under a general framework. Indeed, there is no specific type of reinsurance contract, there is no specific dynamics of the involved financial instruments and the financial market does not have to be free of frictions. On the other hand, it will be pointed out how the optimal combination above may provide us with new premium principles making the insurer global risk vanish. The risk will be managed with a coherent risk measure, and the new premium principles will seem to reflect several properties, which are desirable from both the analytical and the economic perspectives. From the analytical viewpoint, the premium principles will be continuous, homogeneous and increasing. From the economic viewpoint, the premium principles will lead to cheaper prices with respect to both the insurance market and the financial one. In other words, the premium principles will make the insurer more competitive in prices under a null risk. General necessary and sufficient optimality conditions will be given, as well as closed forms for the solutions under appropriate assumptions. Several methods preventing unbounded optimization problems will warrant special attention, and one particular case will be more thoroughly studied, namely, the combination of the Black–Scholes–Merton pricing model with the conditional value at risk.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79863805","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}
Pub Date : 2022-08-31DOI: 10.1080/03461238.2022.2108335
Wenyuan Wang, D. Muravey, Yang Shen, Yan Zeng
This paper studies a mean-variance investment-reinsurance problem under a new stochastic volatility model, namely the 4/2 stochastic volatility model. Solving this problem requires a deep understanding of a class of parabolic partial differential equations (PPDEs). By the parametrix method and the integral transform method, we derive explicit solutions to the PPDEs in several special cases. Through the Lie symmetry analysis, we obtain a four-parameter family of the 4/2 stochastic volatility models such that the corresponding PPDEs have closed-form solutions. The efficient strategy and the efficient frontier of the mean-variance problem are represented by using the closed-form solutions to PPDEs. Numerical examples for the obtained efficient frontier are provided by Monto Carlo method.
{"title":"Optimal investment and reinsurance strategies under 4/2 stochastic volatility model","authors":"Wenyuan Wang, D. Muravey, Yang Shen, Yan Zeng","doi":"10.1080/03461238.2022.2108335","DOIUrl":"https://doi.org/10.1080/03461238.2022.2108335","url":null,"abstract":"This paper studies a mean-variance investment-reinsurance problem under a new stochastic volatility model, namely the 4/2 stochastic volatility model. Solving this problem requires a deep understanding of a class of parabolic partial differential equations (PPDEs). By the parametrix method and the integral transform method, we derive explicit solutions to the PPDEs in several special cases. Through the Lie symmetry analysis, we obtain a four-parameter family of the 4/2 stochastic volatility models such that the corresponding PPDEs have closed-form solutions. The efficient strategy and the efficient frontier of the mean-variance problem are represented by using the closed-form solutions to PPDEs. Numerical examples for the obtained efficient frontier are provided by Monto Carlo method.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79603918","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}
Pub Date : 2022-08-31DOI: 10.1080/03461238.2022.2108334
Ghislain Léveillé, Ilie-Radu Mitric
We study the moments generating function, moments, distributions, VaR, and TVaR of conditional increments of aggregate discounted claims when the counting process is generated by a trend renewal process. The combined effect of the age process and trend is also examined.
{"title":"Conditional increments of aggregate discounted claims with a trend","authors":"Ghislain Léveillé, Ilie-Radu Mitric","doi":"10.1080/03461238.2022.2108334","DOIUrl":"https://doi.org/10.1080/03461238.2022.2108334","url":null,"abstract":"We study the moments generating function, moments, distributions, VaR, and TVaR of conditional increments of aggregate discounted claims when the counting process is generated by a trend renewal process. The combined effect of the age process and trend is also examined.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87904110","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}
Pub Date : 2022-08-11DOI: 10.1080/03461238.2023.2181708
K. Buchardt, Christian Furrer, Oliver Lunding Sandqvist
ABSTRACT In life insurance contracts, benefits and premiums are typically paid contingent on the biometric state of the insured. Due to delays between the occurrence, reporting, and settlement of changes to the biometric state, the state process is not fully observable in real-time. This fact implies that the classic multi-state models for the biometric state of the insured are not able to describe the development of the policy in real-time, which encompasses handling of incurred-but-not-reported and reported-but-not-settled claims. We give a fundamental treatment of the problem in the setting of continuous-time multi-state life insurance by introducing a new class of models: transaction time models. The relation between the transaction time model and the classic model is studied and a result linking the present values in the two models is derived. The results and their practical implications are illustrated for disability coverages, where we obtain explicit expressions for the transaction time reserve in specific models.
{"title":"Transaction time models in multi-state life insurance","authors":"K. Buchardt, Christian Furrer, Oliver Lunding Sandqvist","doi":"10.1080/03461238.2023.2181708","DOIUrl":"https://doi.org/10.1080/03461238.2023.2181708","url":null,"abstract":"ABSTRACT In life insurance contracts, benefits and premiums are typically paid contingent on the biometric state of the insured. Due to delays between the occurrence, reporting, and settlement of changes to the biometric state, the state process is not fully observable in real-time. This fact implies that the classic multi-state models for the biometric state of the insured are not able to describe the development of the policy in real-time, which encompasses handling of incurred-but-not-reported and reported-but-not-settled claims. We give a fundamental treatment of the problem in the setting of continuous-time multi-state life insurance by introducing a new class of models: transaction time models. The relation between the transaction time model and the classic model is studied and a result linking the present values in the two models is derived. The results and their practical implications are illustrated for disability coverages, where we obtain explicit expressions for the transaction time reserve in specific models.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88517899","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}
Pub Date : 2022-08-01DOI: 10.1080/03461238.2022.2099296
Meiqiao Ai, Zhimin Zhang, Dan Zhu
Variable annuities with complex surrender features are nowadays increasingly popular for managing longevity risks. The study of their accurate pricing and sensitivity analysis is one of the main actuarial research topics. This paper studies the valuation problem of variable annuity contracts with guaranteed minimum maturity benefits on a set of predetermined discrete tenor dates under regime-switching Lévy models. Extending from existing vanilla payoffs, we consider the guaranteed minimum maturity benefits with lookback and geometric average features. We customise the dynamic programming principle to solve the corresponding optimal stopping problem, relying on some semi-analytical valuation formulae resulting from an acute Fourier cosine series expansion. Finally, numerical illustrations are provided to show the accuracy and efficiency of the proposed method. We also demonstrate the use of our proposed method in a range of sensitivity analysis exercises, which shed light on the pricing and risk management of complex variable annuity products.
{"title":"Valuing variable annuities with path-dependent surrender guarantees under regime-switching Lévy models","authors":"Meiqiao Ai, Zhimin Zhang, Dan Zhu","doi":"10.1080/03461238.2022.2099296","DOIUrl":"https://doi.org/10.1080/03461238.2022.2099296","url":null,"abstract":"Variable annuities with complex surrender features are nowadays increasingly popular for managing longevity risks. The study of their accurate pricing and sensitivity analysis is one of the main actuarial research topics. This paper studies the valuation problem of variable annuity contracts with guaranteed minimum maturity benefits on a set of predetermined discrete tenor dates under regime-switching Lévy models. Extending from existing vanilla payoffs, we consider the guaranteed minimum maturity benefits with lookback and geometric average features. We customise the dynamic programming principle to solve the corresponding optimal stopping problem, relying on some semi-analytical valuation formulae resulting from an acute Fourier cosine series expansion. Finally, numerical illustrations are provided to show the accuracy and efficiency of the proposed method. We also demonstrate the use of our proposed method in a range of sensitivity analysis exercises, which shed light on the pricing and risk management of complex variable annuity products.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82920221","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：