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Methodology and Computing in Applied Probability最新文献

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Conditional Moment Matching and Stratified Approximation for Pricing and Hedging Periodic-Premium Variable Annuities 用于定期保费变额年金定价和对冲的条件矩匹配和分层逼近法
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-04-11 DOI: 10.1007/s11009-024-10082-1
Xiao Wei, Xingchi Gu
{"title":"Conditional Moment Matching and Stratified Approximation for Pricing and Hedging Periodic-Premium Variable Annuities","authors":"Xiao Wei, Xingchi Gu","doi":"10.1007/s11009-024-10082-1","DOIUrl":"https://doi.org/10.1007/s11009-024-10082-1","url":null,"abstract":"<p>This paper extends the stratified approximation method using lognormal and gamma distributions - first introduced to price Asian options - to derive a close formula for pricing and hedging of periodic-premium variable annuities. We used the moment matching method to fit the lognormal and gamma distributions to the conditional distribution of the integral of the underlying asset on a time interval, given the terminal value of the underlying asset. The highly oscillating double integrals for computing an expectation about the integral of the underlying assets are simplified down to a single integral, which greatly reduces the computation time for pricing periodic-premium variable annuities. This method allowed us to construct a different delta hedging strategy, other than the one used in the existing literature for embedded option of periodic-premium variable annuities. Compared with the existing research on pricing periodic-premium variable annuities, we obtained more accurate results using the stratified approximation method than the numerical method of partial differential equations, and found that the underpricing problem with periodic-premium variable annuities is even more severe than previously stated in existing literature. We further investigated the price gap between single-premium and periodic-premium variable annuities in a variety of settings, and examined the impact that the model and product parameters had on the price gap. The robustness and accuracy of the proposed method is tested by numerical examples.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"44 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Valuation at Origination of Mortgages with Full Prepayment and Default Risks 具有完全预付和违约风险的抵押贷款的初始估值
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-04-08 DOI: 10.1007/s11009-024-10081-2
Congjin Zhou, Guojing Wang, Yinghui Dong, Pin Wang
{"title":"The Valuation at Origination of Mortgages with Full Prepayment and Default Risks","authors":"Congjin Zhou, Guojing Wang, Yinghui Dong, Pin Wang","doi":"10.1007/s11009-024-10081-2","DOIUrl":"https://doi.org/10.1007/s11009-024-10081-2","url":null,"abstract":"<p>We investigate the valuation problem of a mortgage contract with full prepayment and default risks using the reduced-form model with regime switching. The hazard rates of full prepayment and default are specified as linear functions of the risk-free interest rate and house prices, respectively, which are characterized by Ornstein-Uhlenbeck processes with regime switching. To derive the explicit valuation formula, we derive the distribution of the number of transitions for two-state Markov processes in finite time and the conditional joint probability density function of transition times using the uniformization technique. Finally, we analyze the effect of parameters on the valuation of the mortgage.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"77 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Pricing Strategy in an Unreliable M/M/1 Retrial Queue with Delayed Repair and Breakdown Deterioration 具有延迟修复和故障恶化的不可靠 M/M/1 重审队列中的最优定价策略
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-04-05 DOI: 10.1007/s11009-024-10080-3
Fan Xu, Ruiling Tian, Qi Shao
{"title":"Optimal Pricing Strategy in an Unreliable M/M/1 Retrial Queue with Delayed Repair and Breakdown Deterioration","authors":"Fan Xu, Ruiling Tian, Qi Shao","doi":"10.1007/s11009-024-10080-3","DOIUrl":"https://doi.org/10.1007/s11009-024-10080-3","url":null,"abstract":"<p>This paper focuses on an unreliable M/M/1 retrial queue with delayed repair, in which a novel breakdown mechanism is considered, i.e., a normal breakdown may deteriorate into a major breakdown. Arriving customers are not provided with the system’s information, but must decide whether or not to join it. First, the steady state of the system is analyzed. Then, based on the practical requirements of the cloud computing system, we construct an optimization model to minimize the response time of requesting information with proportions of detection, and repair of the normal and major breakdown as the decision variable. Furthermore, equilibrium joining strategies and the socially optimal pricing strategy are studied from the perspectives of the customer and the social planner, respectively. Finally, numerical examples are used to illustrate the impact of different parameters on strategies.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"14 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Approximations for Utility-Based Pricing 基于效用的定价的高效近似值
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-03-28 DOI: 10.1007/s11009-024-10076-z
{"title":"Efficient Approximations for Utility-Based Pricing","authors":"","doi":"10.1007/s11009-024-10076-z","DOIUrl":"https://doi.org/10.1007/s11009-024-10076-z","url":null,"abstract":"<h3>Abstract</h3> <p>In a context of illiquidity, the reservation price is a well-accepted alternative to the usual martingale approach which does not apply. However, this price is not available in closed form and requires numerical methods such as Monte Carlo or polynomial approximations to evaluate it. We show that these methods can be inaccurate and propose a deterministic decomposition of the reservation price using the Lambert function. This decomposition allows us to perform an improved Monte Carlo method, which we name Lambert Monte Carlo (LMC) and to give deterministic approximations of the reservation price and of the optimal strategies based on the Lambert function. We also give an answer to the problem of selecting a hedging asset that minimizes the reservation price and also the cash invested. Our theoretical results are illustrated by numerical simulations.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"92 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140324710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reconstruction of Random Fields Concentrated on an Unknown Curve using Irregularly Sampled Data 利用不规则采样数据重构集中在未知曲线上的随机场
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-03-14 DOI: 10.1007/s11009-024-10079-w
Guillaume Perrin, Christian Soize
{"title":"Reconstruction of Random Fields Concentrated on an Unknown Curve using Irregularly Sampled Data","authors":"Guillaume Perrin, Christian Soize","doi":"10.1007/s11009-024-10079-w","DOIUrl":"https://doi.org/10.1007/s11009-024-10079-w","url":null,"abstract":"<p>In the world of connected automated objects, increasingly rich and structured data are collected daily (positions, environmental variables, etc.). In this work, we are interested in the characterization of the variability of the trajectories of one of these objects (robot, drone, or delivery droid for example) along a particular path from irregularly sampled data in time and space. To do so, we model the position of the considered object by a random field indexed in time, whose distribution we try to estimate (for risk analysis for example). This distribution being by construction concentrated on an unknown curve, two phases are proposed for its reconstruction: a phase of identification of this curve, by clustering and polynomial smoothing techniques, then a phase of statistical inference of the random field orthogonal to this curve, by spectral methods and kernel reconstructions. The efficiency of the proposed approach, both in terms of computation time and reconstruction quality, is illustrated on several numerical applications.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reliability and Optimization for k-out-of-n: G Mixed Standby Retrial System with Dependency and J-Vacation k-out-of-n：G 混合备用重试系统与依赖性和 J-空缺
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-02-28 DOI: 10.1007/s11009-024-10078-x
Qi Shao, Linmin Hu, Fan Xu
{"title":"Reliability and Optimization for k-out-of-n: G Mixed Standby Retrial System with Dependency and J-Vacation","authors":"Qi Shao, Linmin Hu, Fan Xu","doi":"10.1007/s11009-024-10078-x","DOIUrl":"https://doi.org/10.1007/s11009-024-10078-x","url":null,"abstract":"<p>Based on the design and potential application of wind-solar storage intelligent power generation systems in engineering practice, this paper develops a novel reliability model of <i>k</i>-out-of-<i>n</i>: G mixed standby retrial system with failure dependency and <i>J</i>-vacation policy. The working components in the system have redundant dependencies. When any component of the system fails and the repairman is working or on vacation, the failed component goes into the retrial space. If the retrial space has no failed components, the idle repairman goes on vacation, which may last for up to <i>J</i> consecutive vacations, until at a minimum one failed component appears in the retrial space on a vacation return. Firstly, the performance indexes of the system under steady state are analyzed based on the Markov process theory. Secondly, an algorithm for modelling the failure process of the proposed model is developed through a Monte Carlo method, and numerical solutions for the reliability function and mean time to first failure (MTTFF) are presented. Then, some numerical examples are provided to demonstrate the influence of different parameters on the system reliability indexes. Finally, a system cost optimization model based on availability control is developed, and the optimal component configuration schemes for systems with no vacations and different maximum numbers of vacations <i>J</i> are compared and analyzed by genetic algorithm (GA).</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"38 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-zero-sum Stochastic Differential Games for Asset-Liability Management with Stochastic Inflation and Stochastic Volatility 具有随机通胀和随机波动性的资产负债管理非零和随机差分博弈
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-02-22 DOI: 10.1007/s11009-024-10072-3
{"title":"Non-zero-sum Stochastic Differential Games for Asset-Liability Management with Stochastic Inflation and Stochastic Volatility","authors":"","doi":"10.1007/s11009-024-10072-3","DOIUrl":"https://doi.org/10.1007/s11009-024-10072-3","url":null,"abstract":"<h3>Abstract</h3> <p>This paper investigates the optimal asset-liability management problems for two managers subject to relative performance concerns in the presence of stochastic inflation and stochastic volatility. The objective of the two managers is to maximize the expected utility of their relative terminal surplus with respect to that of their competitor. The problem of finding the optimal investment strategies for both managers is modeled as a non-zero-sum stochastic differential game. Both managers have access to a financial market consisting of a risk-free asset, a risky asset, and an inflation-linked index bond. The risky asset’s price process and uncontrollable random liabilities are not only affected by the inflation risk but also driven by a general class of stochastic volatility models embracing the constant elasticity of variance model, the family of state-of-the-art 4/2 models, and some path-dependent models. By adopting a backward stochastic differential equation (BSDE) approach to overcome the possibly non-Markovian setting, closed-form expressions for the equilibrium investment strategies and the corresponding value functions are derived under power and exponential utility preferences. Moreover, explicit solutions to some special cases of our model are provided. Finally, we perform numerical studies to illustrate the influence of relative performance concerns on the equilibrium strategies and draw some economic interpretations.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"43 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139954443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Survival of Coherent Systems Subject to Random Shocks 论受到随机冲击的相干系统的生存问题
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-02-19 DOI: 10.1007/s11009-024-10077-y
Dheeraj Goyal, Nil Kamal Hazra, Maxim Finkelstein
{"title":"On Survival of Coherent Systems Subject to Random Shocks","authors":"Dheeraj Goyal, Nil Kamal Hazra, Maxim Finkelstein","doi":"10.1007/s11009-024-10077-y","DOIUrl":"https://doi.org/10.1007/s11009-024-10077-y","url":null,"abstract":"<p>We consider coherent systems subject to random shocks that can damage a random number of components of a system. Based on the distribution of the number of failed components, we discuss three models, namely, (<i>i</i>) a shock can damage any number of components (including zero) with the same probability, (<i>ii</i>) each shock damages, at least, one component, and (<i>iii</i>) a shock can damage, at most, one component. Shocks arrival times are modeled using three important counting processes, namely, the Poisson generalized gamma process, the Poisson phase-type process and the renewal process with matrix Mittag-Leffler distributed inter-arrival times. For the defined shock models, we discuss relevant reliability properties of coherent systems. An optimal replacement policy for repairable systems is considered as an application of the proposed modeling.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"25 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139910363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How Many Digits are Needed? 需要多少位数？
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-02-08 DOI: 10.1007/s11009-024-10073-2
Ira W. Herbst, Jesper Møller, Anne Marie Svane
{"title":"How Many Digits are Needed?","authors":"Ira W. Herbst, Jesper Møller, Anne Marie Svane","doi":"10.1007/s11009-024-10073-2","DOIUrl":"https://doi.org/10.1007/s11009-024-10073-2","url":null,"abstract":"<p>Let <span>(X_1,X_2,...)</span> be the digits in the base-<i>q</i> expansion of a random variable <i>X</i> defined on [0, 1) where <span>(qge 2)</span> is an integer. For <span>(n=1,2,...)</span>, we study the probability distribution <span>(P_n)</span> of the (scaled) remainder <span>(T^n(X)=sum _{k=n+1}^infty X_k q^{n-k})</span>: If <i>X</i> has an absolutely continuous CDF then <span>(P_n)</span> converges in the total variation metric to the Lebesgue measure <span>(mu )</span> on the unit interval. Under weak smoothness conditions we establish first a coupling between <i>X</i> and a non-negative integer valued random variable <i>N</i> so that <span>(T^N(X))</span> follows <span>(mu )</span> and is independent of <span>((X_1,...,X_N))</span>, and second exponentially fast convergence of <span>(P_n)</span> and its PDF <span>(f_n)</span>. We discuss how many digits are needed and show examples of our results.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"20 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit 具有多个服务节点的队列盘存系统和从共同轨道出发的寻址重访系统
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-02-02 DOI: 10.1007/s11009-023-10071-w
{"title":"Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit","authors":"","doi":"10.1007/s11009-023-10071-w","DOIUrl":"https://doi.org/10.1007/s11009-023-10071-w","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we consider a queueing inventory model with <em>K</em> service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (<em>s</em>, <em>S</em>) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"19 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139670162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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