Pub Date : 2023-01-26DOI: 10.1017/s0269964822000535
Shuyang Gao, Rafik Aguech
In this study, we consider a class of multiple-drawing opposite-reinforcing urns with time-dependent replacement rules. The class has the symmetric property of a Friedman-type urn. We divide the class into a small-increment regime and a large-increment regime. For small-increment schemes, we prove almost-sure convergence and a central limit theorem for the proportion of white balls by stochastic approximation. For large-increment schemes, by assuming the affinity condition, we show almost-sure convergence of the proportion of white balls by martingale theory and present a way to identify the limit distribution of the proportion of white balls.
{"title":"Multiple-drawing dynamic Friedman urns with opposite-reinforcement","authors":"Shuyang Gao, Rafik Aguech","doi":"10.1017/s0269964822000535","DOIUrl":"https://doi.org/10.1017/s0269964822000535","url":null,"abstract":"\u0000 In this study, we consider a class of multiple-drawing opposite-reinforcing urns with time-dependent replacement rules. The class has the symmetric property of a Friedman-type urn. We divide the class into a small-increment regime and a large-increment regime. For small-increment schemes, we prove almost-sure convergence and a central limit theorem for the proportion of white balls by stochastic approximation. For large-increment schemes, by assuming the affinity condition, we show almost-sure convergence of the proportion of white balls by martingale theory and present a way to identify the limit distribution of the proportion of white balls.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83056402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-20DOI: 10.1017/s0269964823000013
Zhuoting Yu, S. Andradóttir, H. Ayhan
We consider a two-stage service system with two types of servers, namely subordinates who perform the first-stage service and supervisors who have their own responsibilities in addition to collaborating with the subordinates on the second-stage service. Rewards are earned when first- or second-stage service is completed and when supervisors finish one of their own responsibilities. Costs are incurred when impatient customers abandon without completing the second-stage service. Our problem is to determine how the supervisors should distribute their time between their joint work with the subordinates and their own responsibilities. Under the assumptions that service times at both stages are exponentially distributed and that the customers waiting for second-stage service abandon after an exponential amount of time, we prove that one of two policies will maximize the long-run average profit. Namely, it is optimal for supervisors to start collaborating with subordinates either when subordinates can no longer serve new customers or as soon as there is a customer ready for second-stage service. Furthermore, we show that the optimality condition is a simple threshold on the system parameters. We conclude by proving that pooling supervisors (and their associated subordinates) improves system performance, but with limited returns as more supervisors are pooled.
{"title":"Optimal control of supervisors balancing individual and joint responsibilities","authors":"Zhuoting Yu, S. Andradóttir, H. Ayhan","doi":"10.1017/s0269964823000013","DOIUrl":"https://doi.org/10.1017/s0269964823000013","url":null,"abstract":"\u0000 We consider a two-stage service system with two types of servers, namely subordinates who perform the first-stage service and supervisors who have their own responsibilities in addition to collaborating with the subordinates on the second-stage service. Rewards are earned when first- or second-stage service is completed and when supervisors finish one of their own responsibilities. Costs are incurred when impatient customers abandon without completing the second-stage service. Our problem is to determine how the supervisors should distribute their time between their joint work with the subordinates and their own responsibilities. Under the assumptions that service times at both stages are exponentially distributed and that the customers waiting for second-stage service abandon after an exponential amount of time, we prove that one of two policies will maximize the long-run average profit. Namely, it is optimal for supervisors to start collaborating with subordinates either when subordinates can no longer serve new customers or as soon as there is a customer ready for second-stage service. Furthermore, we show that the optimality condition is a simple threshold on the system parameters. We conclude by proving that pooling supervisors (and their associated subordinates) improves system performance, but with limited returns as more supervisors are pooled.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"21 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73992750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-10DOI: 10.1017/s0269964822000493
Xenos Chang-Shuo Lin, D. Miao, Ying-I Lee, Yu Zheng
This paper extends the standard double-exponential jump-diffusion (DEJD) model to allow for successive jumps to bring about different effects on the asset price process. The double-exponentially distributed jump sizes are no longer assumed to have the same parameters; instead, we assume that these parameters may take a series of different values to reflect growing or diminishing effects from these jumps. The mathematical analysis of the stock price requires an introduction of a number of distributions that are extended from the hypoexponential (HE) distribution. Under such a generalized setting, the European option price is derived in closed-form which ensures its computational convenience. Through our numerical examples, we examine the effects on the return distributions from the growing and diminishing severity of the upcoming jumps expected in the near future, and investigate how the option prices and the shapes of the implied volatility smiles are influenced by the varying severity of jumps. These results demonstrate the benefits of the modeling flexibility provided by our extension.
{"title":"Option pricing under a double-exponential jump-diffusion model with varying severity of jumps","authors":"Xenos Chang-Shuo Lin, D. Miao, Ying-I Lee, Yu Zheng","doi":"10.1017/s0269964822000493","DOIUrl":"https://doi.org/10.1017/s0269964822000493","url":null,"abstract":"This paper extends the standard double-exponential jump-diffusion (DEJD) model to allow for successive jumps to bring about different effects on the asset price process. The double-exponentially distributed jump sizes are no longer assumed to have the same parameters; instead, we assume that these parameters may take a series of different values to reflect growing or diminishing effects from these jumps. The mathematical analysis of the stock price requires an introduction of a number of distributions that are extended from the hypoexponential (HE) distribution. Under such a generalized setting, the European option price is derived in closed-form which ensures its computational convenience. Through our numerical examples, we examine the effects on the return distributions from the growing and diminishing severity of the upcoming jumps expected in the near future, and investigate how the option prices and the shapes of the implied volatility smiles are influenced by the varying severity of jumps. These results demonstrate the benefits of the modeling flexibility provided by our extension.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86860863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-09DOI: 10.1017/S0269964822000468
J. S. Li, Joseph H. T. Kim
In the context of mortality forecasting, “rotation” refers to the phenomenon that mortality decline accelerates at older ages but decelerates at younger ages. Since rotation is typically subtle, it is difficult to be confirmed and modeled in a statistical, data-driven manner. In this paper, we attempt to overcome this challenge by proposing an alternative modeling approach. The approach encompasses a new model structure, which includes a component that is devoted to measuring rotation. It also features a modeling technique known as ANCOVA, which allows us to statistically detect rotation and extrapolate the phenomenon into the future. Our proposed approach yields plausible mortality forecasts that are similar to those produced by Li et al. [Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections. Demography 50 (6), 2037–205, and may be considered more advantageous than the approach of Li et al. in the sense that it is able to generate not only static but also stochastic forecasts.
{"title":"Rotation in age patterns of mortality decline: statistical evidence and modeling","authors":"J. S. Li, Joseph H. T. Kim","doi":"10.1017/S0269964822000468","DOIUrl":"https://doi.org/10.1017/S0269964822000468","url":null,"abstract":"In the context of mortality forecasting, “rotation” refers to the phenomenon that mortality decline accelerates at older ages but decelerates at younger ages. Since rotation is typically subtle, it is difficult to be confirmed and modeled in a statistical, data-driven manner. In this paper, we attempt to overcome this challenge by proposing an alternative modeling approach. The approach encompasses a new model structure, which includes a component that is devoted to measuring rotation. It also features a modeling technique known as ANCOVA, which allows us to statistically detect rotation and extrapolate the phenomenon into the future. Our proposed approach yields plausible mortality forecasts that are similar to those produced by Li et al. [Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections. Demography 50 (6), 2037–205, and may be considered more advantageous than the approach of Li et al. in the sense that it is able to generate not only static but also stochastic forecasts.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"34 1","pages":"621 - 652"},"PeriodicalIF":1.1,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79064332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-09DOI: 10.1017/S0269964822000481
K. Hu, Jingchao Li, Jieming Zhou
Abstract In this paper, we consider a mixed dividend strategy in a dual risk model. The mixed dividend strategy is the combination of a threshold dividend and a Parisian implementation delays dividend under periodic observation. Given a series of discrete observation points, when the surplus level is larger than the predetermined bonus barrier at observation point, the Parisian implementation delays dividend is immediately carried out, and the threshold dividend is performed continuously during the delayed period. We study the Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments before ruin in such a dual risk model. Numerical illustrations are given to study the influence of relevant parameters on the ruin-related quantities and the selection of the optimal dividend barrier for a given initial surplus level.
{"title":"On the dual risk model with Parisian implementation delays under a mixed dividend strategy","authors":"K. Hu, Jingchao Li, Jieming Zhou","doi":"10.1017/S0269964822000481","DOIUrl":"https://doi.org/10.1017/S0269964822000481","url":null,"abstract":"Abstract In this paper, we consider a mixed dividend strategy in a dual risk model. The mixed dividend strategy is the combination of a threshold dividend and a Parisian implementation delays dividend under periodic observation. Given a series of discrete observation points, when the surplus level is larger than the predetermined bonus barrier at observation point, the Parisian implementation delays dividend is immediately carried out, and the threshold dividend is performed continuously during the delayed period. We study the Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments before ruin in such a dual risk model. Numerical illustrations are given to study the influence of relevant parameters on the ruin-related quantities and the selection of the optimal dividend barrier for a given initial surplus level.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"32 1","pages":"442 - 461"},"PeriodicalIF":1.1,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88736604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-09DOI: 10.1017/s0269964822000511
Xingyu Yan, Hao-Gang Wang, Hong Sun, Peng Zhao
This paper develops the estimation method of mean and covariance functions of functional data with additional covariate information. With the strength of both local linear smoothing modeling and general weighing scheme, we are able to explicitly characterize the mean and covariance functions with incorporating covariate for irregularly spaced and sparsely observed longitudinal data, as typically encountered in engineering technology or biomedical studies, as well as for functional data which are densely measured. Theoretically, we establish the uniform convergence rates of the estimators in the general weighing scheme. Monte Carlo simulation is conducted to investigate the finite-sample performance of the proposed approach. Two applications including the children growth data and white matter tract dataset obtained from Alzheimer's Disease Neuroimaging Initiative study are also provided.
{"title":"Incorporating covariate into mean and covariance function estimation of functional data under a general weighing scheme","authors":"Xingyu Yan, Hao-Gang Wang, Hong Sun, Peng Zhao","doi":"10.1017/s0269964822000511","DOIUrl":"https://doi.org/10.1017/s0269964822000511","url":null,"abstract":"This paper develops the estimation method of mean and covariance functions of functional data with additional covariate information. With the strength of both local linear smoothing modeling and general weighing scheme, we are able to explicitly characterize the mean and covariance functions with incorporating covariate for irregularly spaced and sparsely observed longitudinal data, as typically encountered in engineering technology or biomedical studies, as well as for functional data which are densely measured. Theoretically, we establish the uniform convergence rates of the estimators in the general weighing scheme. Monte Carlo simulation is conducted to investigate the finite-sample performance of the proposed approach. Two applications including the children growth data and white matter tract dataset obtained from Alzheimer's Disease Neuroimaging Initiative study are also provided.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"118 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75764405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-27DOI: 10.1017/s026996482200050x
Yihao Pan, D. Tang, Xingchun Wang
In this paper, we investigate the pricing of vulnerable European options in a market where the underlying stocks are not perfectly liquid. A liquidity discount factor is used to model the effect of liquidity risk in the market, and the default risk of the option issuer is incorporated into the model using a reduced-form model, where the default intensity process is correlated with the liquidity risk. We obtain a semiclosed-form pricing formula of vulnerable options through the inverse Fourier transform. Finally, we illustrate the effects of default risk and liquidity risk on option prices numerically.
{"title":"Valuation of vulnerable European options with market liquidity risk","authors":"Yihao Pan, D. Tang, Xingchun Wang","doi":"10.1017/s026996482200050x","DOIUrl":"https://doi.org/10.1017/s026996482200050x","url":null,"abstract":"\u0000 In this paper, we investigate the pricing of vulnerable European options in a market where the underlying stocks are not perfectly liquid. A liquidity discount factor is used to model the effect of liquidity risk in the market, and the default risk of the option issuer is incorporated into the model using a reduced-form model, where the default intensity process is correlated with the liquidity risk. We obtain a semiclosed-form pricing formula of vulnerable options through the inverse Fourier transform. Finally, we illustrate the effects of default risk and liquidity risk on option prices numerically.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88919718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-29DOI: 10.1017/s0269964822000407
P. Pasricha, Xin‐Jiang He
Zhu and He [(2018). A new closed-form formula for pricing European options under a skew Brownian motion. The European Journal of Finance 24(12): 1063–1074] provided an innovative closed-form solution by replacing the standard Brownian motion in the Black–Scholes framework using a particular skew Brownian motion. Their formula involves numerically integrating the product of the Guassian density and corresponding distribution function. Being different from their pricing formula, we derive a much simpler formula that only involves the Gaussian distribution function and Owen's $T$ function.
{"title":"A simple European option pricing formula with a skew Brownian motion","authors":"P. Pasricha, Xin‐Jiang He","doi":"10.1017/s0269964822000407","DOIUrl":"https://doi.org/10.1017/s0269964822000407","url":null,"abstract":"Zhu and He [(2018). A new closed-form formula for pricing European options under a skew Brownian motion. The European Journal of Finance 24(12): 1063–1074] provided an innovative closed-form solution by replacing the standard Brownian motion in the Black–Scholes framework using a particular skew Brownian motion. Their formula involves numerically integrating the product of the Guassian density and corresponding distribution function. Being different from their pricing formula, we derive a much simpler formula that only involves the Gaussian distribution function and Owen's \u0000 \u0000 \u0000 $T$\u0000 \u0000 function.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90928661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-29DOI: 10.1017/s0269964822000444
Zhenfeng Zou, Zichao Xia, Taizhong Hu
Motivated by Ahmadi-Javid (Journal of Optimization Theory Applications, 155(3), 2012, 1105–1123) and Ahmadi-Javid and Pichler (Mathematics and Financial Economics, 11, 2017, 527–550), the concept of Tsallis Value-at-Risk (TsVaR) based on Tsallis entropy is introduced in this paper. TsVaR corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the Value-at-Risk. The main properties and analogous dual representation of TsVaR are investigated. These results partially generalize the Entropic Value-at-Risk by involving Tsallis entropies. Three spaces, called the primal, dual, and bidual Tsallis spaces, corresponding to TsVaR are fully studied. It is shown that these spaces equipped with the norm induced by TsVaR are Banach spaces. The Tsallis spaces are related to the $L^p$ spaces, as well as specific Orlicz hearts and Orlicz spaces. Finally, we derive explicit formula for the dual TsVaR norm.
本文在Ahmadi-Javid(优化理论应用，155(3)，2012,1105-1123)和Ahmadi-Javid and Pichler(数学与金融经济学，11,2017,527-550)的激励下，引入了基于Tsallis熵的Tsallis风险价值(TsVaR)概念。TsVaR对应于由Chernoff不等式得到的风险价值的最紧可能上界。研究了TsVaR的主要性质和类似对偶表示。这些结果通过涉及Tsallis熵部分地推广了风险熵。充分研究了与TsVaR相对应的三个空间，即原始、对偶和双Tsallis空间。结果表明，这些具有TsVaR诱导范数的空间是Banach空间。Tsallis空间与$L^p$空间以及特定的Orlicz心和Orlicz空间有关。最后，我们导出了对偶TsVaR范数的显式公式。
{"title":"Tsallis value-at-risk: generalized entropic value-at-risk","authors":"Zhenfeng Zou, Zichao Xia, Taizhong Hu","doi":"10.1017/s0269964822000444","DOIUrl":"https://doi.org/10.1017/s0269964822000444","url":null,"abstract":"\u0000 Motivated by Ahmadi-Javid (Journal of Optimization Theory Applications, 155(3), 2012, 1105–1123) and Ahmadi-Javid and Pichler (Mathematics and Financial Economics, 11, 2017, 527–550), the concept of Tsallis Value-at-Risk (TsVaR) based on Tsallis entropy is introduced in this paper. TsVaR corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the Value-at-Risk. The main properties and analogous dual representation of TsVaR are investigated. These results partially generalize the Entropic Value-at-Risk by involving Tsallis entropies. Three spaces, called the primal, dual, and bidual Tsallis spaces, corresponding to TsVaR are fully studied. It is shown that these spaces equipped with the norm induced by TsVaR are Banach spaces. The Tsallis spaces are related to the \u0000 \u0000 \u0000 $L^p$\u0000 \u0000 spaces, as well as specific Orlicz hearts and Orlicz spaces. Finally, we derive explicit formula for the dual TsVaR norm.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"61 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80611417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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