Probability in the Engineering and Informational Sciences最新文献

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A simple European option pricing formula with a skew Brownian motion 一个带有偏布朗运动的简单欧式期权定价公式

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-29 DOI: 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.

朱、何[2018]。偏斜布朗运动下欧式期权定价的新封闭公式。[欧洲金融杂志24(12):1063-1074]通过使用一个特殊的偏布朗运动代替Black-Scholes框架中的标准布朗运动，提供了一个创新的封闭形式解决方案。他们的公式包括对高斯密度和相应分布函数的乘积进行数值积分。与他们的定价公式不同，我们推导了一个更简单的公式，只涉及高斯分布函数和欧文的$T$函数。

引用次数: 1

Tsallis value-at-risk: generalized entropic value-at-risk Tsallis风险值:广义熵风险值

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-29 DOI: 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。

引用次数: 1

Optimal allocation of policy limits in layer reinsurance treaties 分层再保险协议中保单限额的最优分配

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-24 DOI: 10.1017/S0269964822000432

Chuchu Wang, Wei Wang, Yiying Zhang, Peng-fei Zhao

Abstract Layer reinsurance treaty is a common form obtained in the problem of optimal reinsurance design. In this paper, we study allocations of policy limits in layer reinsurance treaties with dependent risks. We investigate the effects of orderings and heterogeneity among policy limits on the expected utility functions of the terminal wealth from the viewpoint of risk-averse insurers faced with right tail weakly stochastic arrangement increasing losses. Orderings on optimal allocations are presented for normal layer reinsurance contracts under certain conditions. Parallel studies are also conducted for randomized layer reinsurance contracts. As a special case, the worst allocations of policy limits are also identified when the exact dependence structure among the losses is unknown. Numerical examples are presented to shed light on the theoretical findings.

分层再保险契约是再保险最优设计问题中常见的一种形式。本文研究了具有依赖风险的分层再保险协议中保单限额的分配问题。本文从风险厌恶的角度出发，从右尾弱随机安排增加损失的保险公司的角度，研究了政策限制的排序和异质性对终端财富预期效用函数的影响。在一定条件下，给出了普通层再保险合同的最优分配排序。对随机分层再保险合同也进行了平行研究。作为一种特殊情况，当损失之间的确切依赖结构未知时，还可以确定最坏的政策限额分配。给出了数值例子来阐明理论结论。

引用次数: 0

Mean residual life order among largest order statistics arising from resilience-scale models with reduced scale parameters 基于降尺度参数的弹性尺度模型中最大阶统计量的平均剩余寿命序

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-22 DOI: 10.1017/S0269964821000486

Abedin Haidari, M. Sattari, G. Barmalzan

In this paper, we identify some conditions to compare the largest order statistics from resilience-scale models with reduced scale parameters in the sense of mean residual life order. As an example of the established result, the exponentiated generalized gamma distribution is examined. Also, for the special case of the scale model, power-generalized Weibull and half-normal distributions are investigated.

在平均剩余寿命阶的意义上，我们确定了一些条件来比较具有缩减尺度参数的弹性尺度模型的最大阶统计量。作为已建立结果的一个例子，对指数广义伽玛分布进行了检验。对于比例模型的特殊情况，研究了幂广义威布尔分布和半正态分布。

引用次数: 1

Asset allocation for a DC pension plan with minimum guarantee constraint and hidden Markov regime-switching 具有最小担保约束和隐马尔可夫制度切换的DC养老金计划的资产配置

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-21 DOI: 10.1017/s0269964822000419

Liuling Luo, Xingchun Peng

This paper is devoted to the study of the asset allocation problem for a DC pension plan with minimum guarantee constraint in a hidden Markov regime-switching economy. Suppose that four types of assets are available in the financial market: a risk-free asset, a zero-coupon bond, an inflation-indexed bond and a stock. The expected return rate of the stock depends on unobservable economic states, and the change of states is described by a hidden Markov chain. In addition, the CIR process is used to describe the evolution of the nominal interest rate. The contribution rate is also assumed to be stochastic. The goal of investment management is to minimize the convex risk measure of the terminal wealth in excess of the minimum guarantee constraint. First, we transform the partially observable optimization problem into the one with complete information using the Wonham filtering technique and deal with the minimum guarantee constraint by constructing auxiliary processes. Furthermore, we derive the optimal investment strategy by the BSDE approach. Finally, some numerical results are presented to illustrate the impacts of some important parameters on investment behaviors.

本文研究了隐马尔可夫制度切换经济条件下具有最低担保约束的养老金计划的资产配置问题。假设金融市场上有四种类型的资产:无风险资产、零息债券、通胀指数债券和股票。股票的期望收益率依赖于不可观测的经济状态，状态的变化用隐马尔可夫链来描述。此外，还利用CIR过程来描述名义利率的演变。贡献率也被假定为随机的。投资管理的目标是使终端财富超过最低担保约束的凸风险测度最小化。首先，利用Wonham滤波技术将部分可观察优化问题转化为完全信息优化问题，并通过构造辅助过程来处理最小保证约束。在此基础上，利用BSDE方法推导出最优投资策略。最后，给出了一些数值结果来说明一些重要参数对投资行为的影响。

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引用次数: 1

Resolving an open problem on the hazard rate ordering of p-spacings 解决了一个关于p间隔的危险率排序的开放性问题

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-11 DOI: 10.1017/s0269964822000377

Mahdi Alimohammadi

Let $V_{(r,n,tilde {m}_n,k)}^{(p)}$ and $W_{(r,n,tilde {m}_n,k)}^{(p)}$ be the $p$-spacings of generalized order statistics based on absolutely continuous distribution functions $F$ and $G$, respectively. Imposing some conditions on $F$ and $G$ and assuming that $m_1=cdots =m_{n-1}$, Hu and Zhuang (2006. Stochastic orderings between p-spacings of generalized order statistics from two samples. Probability in the Engineering and Informational Sciences 20: 475) established $V_{(r,n,tilde {m}_n,k)}^{(p)} leq _{{rm hr}} W_{(r,n,til

设$V_{(r,n,tilde {m}_n,k)}^{(p)}$和$W_{(r,n,tilde {m}_n,k)}^{(p)}$分别为基于绝对连续分布函数$F$和$G$的广义序统计量的$p$ -间距。对$F$和$G$施加一定条件，并假设$m_1=cdots =m_{n-1}$, Hu and Zhuang(2006)。两样本广义序统计量p-间隔间的随机排序。工程与信息科学中的概率(20:475)为$p=1$建立了$V_{(r,n,tilde {m}_n,k)}^{(p)} leq _{{rm hr}} W_{(r,n,tilde {m}_n,k)}^{(p)}$，并将$pgeq 2$作为一个开放的问题。在本文中，我们不仅解决了这个问题，而且给出了不相等$m_i$的结果。值得一提的是，到目前为止，即使对于普通阶统计量，这个问题也没有得到证明。

引用次数: 0

Analyzing a single hyper-exponential working vacation queue from its governing difference equation 从控制差分方程分析单个超指数休假队列

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-10 DOI: 10.1017/s0269964822000365

Miaomiao Yu, Yinghui Tang

As the queue becomes exhausted, different maintenance tasks can be performed according to the fatigue load and wear degree of the service equipment. At the same time, considering the customer's sensitivity to time delay, the service facility will not completely remain inactive during the maintenance period. To describe this objectively existing phenomenon arising in the waiting line system, we consider a hyper-exponential working vacation queue with a batch renewal arrival process. Through the calculation of the well-structured roots of the associated characteristic equation, the shift operator method in the theory of difference equations and the supplementary variable technique for stochastic modeling plays a central role in the queue-length distribution analysis. Comparison with other ways to analyze queueing models, the advantage of our approach is that we can avoid deriving the complex transition probability matrix of the queue-length process embedded at input points. The feasibility of this approach is verified by extensive numerical examples.

当队列耗尽时，可根据服务设备的疲劳负荷和磨损程度执行不同的维护任务。同时，考虑到客户对时间延迟的敏感性，服务设施不会在维修期间完全处于闲置状态。为了描述这一客观存在于排队系统中的现象，我们考虑了一个具有批量更新到达过程的超指数休假队列。通过计算相关特征方程的结构良好的根，差分方程理论中的位移算子方法和随机建模中的补充变量技术在队列长度分布分析中起着核心作用。与其他分析排队模型的方法相比，该方法的优点是可以避免推导嵌入在输入点的队列长度过程的复杂转移概率矩阵。通过大量的数值算例验证了该方法的可行性。

引用次数: 0

A class of non-zero-sum stochastic differential games between two mean–variance insurers under stochastic volatility 随机波动下两个均值方差保险公司之间的一类非零和随机微分对策

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-11-02 DOI: 10.1017/S0269964822000353

Jiannan Zhang, Ping Chen, Z. Jin, Shuanming Li

This paper studies the open-loop equilibrium strategies for a class of non-zero-sum reinsurance–investment stochastic differential games between two insurers with a state-dependent mean expectation in the incomplete market. Both insurers are able to purchase proportional reinsurance contracts and invest their wealth in a risk-free asset and a risky asset whose price is modeled by a general stochastic volatility model. The surplus processes of two insurers are driven by two standard Brownian motions. The objective for each insurer is to find the equilibrium investment and reinsurance strategies to balance the expected return and variance of relative terminal wealth. Incorporating the forward backward stochastic differential equations (FBSDEs), we derive the sufficient conditions and obtain the general solutions of equilibrium controls for two insurers. Furthermore, we apply our theoretical results to two special stochastic volatility models (Hull–White model and Heston model). Numerical examples are also provided to illustrate our results.

本文研究了不完全市场中具有状态依赖平均期望的两保险人之间的一类非零和再保险投资随机微分对策的开环均衡策略。两家保险公司都可以购买比例再保险合同，并将其财富投资于无风险资产和风险资产，其价格由一般随机波动模型建模。两个保险公司的盈余过程由两个标准布朗运动驱动。每个保险公司的目标是找到平衡的投资和再保险策略，以平衡预期收益和相对终端财富的方差。结合正倒向随机微分方程，导出了两保险公司均衡控制的充分条件和一般解。此外，我们将理论结果应用于两种特殊的随机波动模型(Hull-White模型和Heston模型)。数值算例也说明了我们的结果。

引用次数: 0

Optimal design for network mutual aid 网络互助的优化设计

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-10-31 DOI: 10.1017/S0269964822000341

Jingchao Li, Zichen Fang, Ciyu Nie, Sizhe Chen

Abstract Network mutual aid platforms is one of the popular risk-sharing models in recent years, and they have almost 200 million members in China. However, current mutual aid platforms does not satisfy the actuarial rules in either the apportionment method or the pricing principle. Hence, a variety of mutual aid models which enable mutual aid members with different risks to exchange their risks in a transparent and actuarial fair way have been proposed in this paper. Besides, the decision-making frameworks for participants choosing between the mutual aid platform and similar insurance products, or choosing no risk sharing are constructed, respectively. Decisions are made based on the principle of maximizing expected utility. Moreover, the optimization problems of maximizing profit and minimizing risk are constructed, respectively. Through the principle of individual fairness and relative fairness, the problem of adverse selection of the platform can also be reduced. Finally, the actual mutual aid plan is compared with similar insurance products to discuss the advantages of the optimized plan.

网络互助平台是近年来流行的风险分担模式之一，在中国拥有近2亿会员。然而，目前的互助平台无论是在分摊方式上还是在定价原则上都不符合精算规则。因此，本文提出了多种互助模式，使具有不同风险的互助成员能够以透明和精算公平的方式交换其风险。构建了参与者选择互助平台与同类保险产品、不选择风险共担的决策框架。决策是基于期望效用最大化的原则做出的。并分别构造了利润最大化和风险最小化的优化问题。通过个人公平和相对公平的原则，也可以减少平台逆向选择的问题。最后，将实际互助方案与同类保险产品进行比较，探讨优化方案的优势。

引用次数: 1

A negative binomial approximation in group testing 组检验中的负二项近似

IF 1.1 3区工程技术 Q2 Mathematics

Probability in the Engineering and Informational Sciences

Pub Date : 2022-10-28 DOI: 10.1017/s026996482200033x

Letian Yu, Fraser Daly, Oliver Johnson

We consider the problem of group testing (pooled testing), first introduced by Dorfman. For nonadaptive testing strategies, we refer to a nondefective item as “intruding” if it only appears in positive tests. Such items cause misclassification errors in the well-known COMP algorithm and can make other algorithms produce an error. It is therefore of interest to understand the distribution of the number of intruding items. We show that, under Bernoulli matrix designs, this distribution is well approximated in a variety of senses by a negative binomial distribution, allowing us to understand the performance of the two-stage conservative group testing algorithm of Aldridge.

我们考虑由Dorfman首先提出的群检验问题(pooled检验)。对于非适应性测试策略，如果一个非缺陷项目只出现在阳性测试中，我们将其称为“侵入性”。这些项目会导致著名的COMP算法出现误分类错误，并可能使其他算法产生错误。因此，了解入侵项目的数量分布是很有意义的。我们表明，在伯努利矩阵设计下，该分布在各种意义上都可以被负二项分布很好地近似，这使我们能够理解Aldridge的两阶段保守群检验算法的性能。

引用次数: 1

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