Continuous-Time Models for Firm Valuation and Their Collateral Effect on Risk-Neutral Probabilities and No-Arbitraging Principle

Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to negatively skewed ones,and their means are concave-down functions of time.When payments are set to zero or proportional to the firm value,EMM turns into the Geometric Brownian model(GBM).We show that risk-neutral probabilities(RNPs)and the no-arbitraging principle(NAP)follow from GBM.When firm’s payments are considered,RNPs and NAP hold for the entire market for short times only,but for long-term investments,RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant,and fail when the mean year returns decline.The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.

Recovering implied risk-neutral probability density function using SVR

Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.

Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Earthquake detection probabilities and completeness magnitude in the northern margin of the Ordos Block

The assessment of the completeness of earthquake catalogs is a prerequisite for studying the patterns of seismic activity.In traditional approaches,the minimum magnitude of completeness(MC)is employed to evaluate catalog completeness,with events below MC being discarded,leading to the underutilization of the data.Detection probability is a more detailed measure of the catalog's completeness than MC;its use results in better model compatibility with data in seismic activity modeling and allows for more comprehensive utilization of seismic observation data across temporal,spatial,and magnitude dimensions.Using the magnitude-rank method and Maximum Curvature(MAXC)methods,we analyzed temporal variations in earthquake catalog completeness,fi nding that MC stabilized after 2010,which closely coincides with improvements in monitoring capabilities and the densifi cation of seismic networks.Employing the probability-based magnitude of completeness(PMC)and entire magnitude range(EMR)methods,grounded in distinct foundational assumptions and computational principles,we analyzed the 2010-2023 earthquake catalog for the northern margin of the Ordos Block,aiming to assess the detection probability of earthquakes and the completeness of the earthquake catalog.The PMC method yielded the detection probability distribution for 76 stations in the distance-magnitude space.A scoring metric was designed based on station detection capabilities for small earthquakes in the near fi eld.From the detection probabilities of stations,we inferred detection probabilities of the network for diff erent magnitude ranges and mapped the spatial distribution of the probability-based completeness magnitude.In the EMR method,we employed a segmented model fi tted to the observed data to determine the detection probability and completeness magnitude for every grid point in the study region.We discussed the sample dependency and low-magnitude failure phenomena of the PMC method,noting the potential overestimation of detection probabilities for lower magnitudes and the underestimation of MC in areas with weaker monitoring capabilities.The results obtained via the two methods support these hypotheses.The assessment results indicate better monitoring capabilities on the eastern side of the study area but worse on the northwest side.The spatial distribution of network monitoring capabilities is uneven,correlating with the distribution of stations and showing signifi cant diff erences in detection capabilities among diff erent stations.The truncation eff ects of data and station selection aff ected the evaluation results at the edges of the study area.Overall,both methods yielded detailed descriptions of the earthquake catalog,but careful selection of calculation parameters or adjustments based on the strengths of diff erent methods is necessary to correct potential biases.

基于概率的震级完备度方法评估云南地震台网的监测能力

为了科学评估云南地震台网的监测能力,分析云南地区的地震监测能力时空分布特征,采用基于概率的震级完备度(PMC)方法,利用2009-2023年云南地震台网地震目录、震相和台站信息等数据,计算了云南地震台网在云南地区的平均地震监测能力和在不同深度的监测能力,得到滇中、滇西局部地区的基于概率的完备性震级M_(P)=1.5,云南全境基本都能监测到2.5级地震。评估了研究时段内云南地震台网台站监测能力的演变,发现部分台站的监测能力持续下降。但自2018年增加20个台站后,云南2.0及2.5级地震的监测范围有一定的扩大,但微震监测能力提升不明显,可能是因为2018年以来云南一直处于小震弱活动状态。最后,对应用PMC方法规划提升台网监测能力进行了展望。

模糊限制语probably的类联接典型范式及其情态功能研究

基于美国当代英语语料库COCA的研究发现:1)与probably共现频数最高的动词、名词和形容词预见了模糊限制语probably最常用的语法构式为"be+probably+adj.+n."与"will/would+probably+v."。2)模糊限制语probably有居中的句法位置趋向,主要发挥认知评价与缓和语气,调节人际关系的语用功能。3)模糊限制语probably的类联接典型范式具有精确话语信息、表达礼貌意义以及传达认知评价的主、客观情态取向的三重情态功能,其情态意义表达强度呈现强弱渐进的变化趋势。

基于蒙特卡罗法的黄土滑坡概率与可靠度分析——以榆林市朝阳路滑坡为例

基于计算滑坡概率的蒙特卡罗法,该文以黄土高原地区的榆林市朝阳路滑坡为研究对象,通过野外调查、室内试验和综合研究,分析了黄土黏聚力和内摩擦角等多种条件下的安全系数分布、失稳概率和可靠度,探讨了参数相关性对于滑坡可靠度的影响,并进行了对黏聚力和内摩擦角的敏感性分析。研究发现,该滑坡为黄土高原区典型降雨诱发型,当同时考虑黏聚力和内摩擦角的变化时,滑坡可靠度指数为1.35,失稳概率为8.83%,安全系数介于0.794~1.305;与同单一变量情况下相比,多个变量分析计算的可靠性指数显著减小,标准偏差明显增大,滑坡失稳概率升高;不同参数相关性条件下,滑坡失稳概率、可靠度和安全系数的标准偏差不同;滑坡的稳定性系数对于不同土性参数的敏感性存在差异。该文基于研究结果提出了相应的防治措施,为黄土高原地区滑坡防治和危险性评估提供科学依据。

probably与maybe的用法比较

初学英语的人,往往把probab—ly(=most likely)一词与maybe(=per-haps)混同起来。但是,无论在意义上还是用法上,两者都有一些差别。首先,在意义方面。

Towards multiple hazard resilient bridges:a methodology for modeling frequent and infrequent time-varying loads Part I,Comprehensive reliability and partial failure probabilities

The current AASHTO load and resistance factor design （LRFD） guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads （also referred to as multiple hazard or MH loads） can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions： （1） formulate the failure probabilities; （2） normalize various load distributions; and （3） establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.

Transition probabilities for NII 2p4f-2p3d and 2s2p^23d-2s2p^23p obtained by a semiclassical method

Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the National Institute of Standards and Technology. The transition probability for a line of 424.18nm is reported for the first time. Meanwhile, a feasible method of calculating transition parameters related to special excited configurations or highly excited states is provided.

低轨增强对北斗量化信号载噪比的影响

为了评估频点兼容下低轨增强对北斗信号接收的影响,从而指导接收机设计,通过概率统计理论推导了低轨增强下北斗信号的量化效应和载噪比损耗模型,并通过蒙特卡罗仿真给出了1~6 bit量化位宽下北斗信号的载噪比损耗与前端增益以及低轨增强功率的关系,仿真与理论结果的一致性较好。实验结果表明,北斗信号最小载噪比损耗对应的最优前端增益与低轨增强功率无关,但最小载噪比衰减值会随着低轨信号功率的增强而增大,1~2 bit量化位宽下有明显的量化损耗,3 bit及以上量化位宽下北斗信号载噪比衰减特性基本一致。

Probable benign paroxysmal positional vertigo, spontaneously resolved:Incidence in medical practice, patients’ characteristics and the natural course

Background: Probable benign paroxysmal positional vertigo, spontaneously resolved (pBPPVsr), is a variant of benign paroxysmal positional vertigo (BPPV) in which there is no observable nystagmus and no vertigo with any positional maneuver. Objectives: To calculate the incidence pBPPVsr, compare the characteristics of the patients with pBPPVsr and BPPV not spontaneously resolved and describe the spontaneous resolution in the natural course of BPPV. Methods: Multicenter prospective descriptive study. During a one-year period, all patients with suspected BPPV that presented to the Neurotology Units of five participating centers were recruited. The incidence of pBPPVsr was calculated as a percentage of the total number of patients with BPPV. The prevalence of several variables was compared between pBPPVsr and BPPV not spontaneously resolved. The timing of spontaneous resolution was estimated using Kaplan-Meier curves. Results: 457 patients met the inclusion criteria. The incidence of pBPPVsr was 33.5%. It was significantly higher in males, in patients with normal bone mass and in patients who were not taking sulpiride. A rate of 18% of spontaneous resolution after the first month and 51% after the first year was found. This percentage did not change in a significant way after this moment. The curves for males, patients under 50 and patients with normal blood pressure decreased significantly faster. Conclusions: In our serie, BPPV spontaneously resolved in half of the patients with BPPV during the first year. This seemed to occur more commonly in males and could have been hindered by sulpiride intake, osteoporosis, advanced age and high blood pressure.

The joint long-term distribution of design environmental factors for offshore structures Multivariate probabilities and simulating method

With the development of ocean engineering, it is one of the most important factors which determine the structural safety, cost and suitable forms of engineerings to select the ocean environmental design criteria. Owing to the complexity , variation and randomness of ocean environmental conditions, the commonly used methods for determining design criteria cannot consider the joint occurring probabilities of several environmental factors ,therefore, lead to overestimate design criteria of them and result in an unnecessary overspend invest in engineering. On the basis of the measured and hindcasting data and the multi-demension joint probability theory, this paper presented the study of the joint loads of wind , wave and current on the offshore structures and its responsible joint probability level with the application of random simulation techniques, and presented the joint design criteria of environmental loads for the realistic design of engineerings.

Theoretical Predictions of Migration Probabilities of Liquid- Liquid Hydrocyclones Separating Light Dispersions

Based on Bloor & Ingham's approach for determining the fluid fieldand on the analyses of loci of fluid particles inside hydrocyclones,analytical models are developed for calculating the migrationprobability of single-cone and two-cone hydrocyclones separatinglight dispersions. The calculated results are in good agreement withThew's correlation at different flow rate, split ratio or fluidproperties if the structural parameters keep the same as those ofThew's 35 mm hydrocyclone. The difference between predictionsaccording to two-cone model and single-cone model is nearlynegligible, which is very close to thew's original idea that majorseparation happens in the small cone-angle zone.

Characteristics of the spatiotemporal distribution of daily extreme temperature events in China:Minimum temperature records in different climate states against the background of the most probable temperature

Based on the skewed function,the most probable temperature is defined and the spatiotemporal distributions of the frequencies and strengths of extreme temperature events in different climate states over China are investigated,where the climate states are referred to as State I,State II and State III,i.e.,the daily minimum temperature records of 1961-1990,1971-2000,and 1981-2009.The results show that in space the frequency of high temperature events in summer decreases clearly in the lower and middle reaches of the Yellow River in State I and that low temperature events decrease in northern China in State II.In the present state,the frequency of high temperature events increases significantly in most areas over China except the north east,while the frequency of low temperature events decreases mainly in north China and the regions between the Yangtze River and the Yellow River.The distributions of frequencies and strengths of extreme temperature events are consistent in space.The analysis of time evolution of extreme events shows that the occurrence of high temperature events become higher with the change in state,while that of low temperature events decreases.High temperature events are becoming stronger as well and deserve to be paid special attention.

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.

On the Exceedance Probabilities of Extreme Drift Motions of An Offshore Structure

The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.

Dynamic Evaluation Strategies for Multiple Aircrafts Formation Using Collision and Matching Probabilities

Configuration evaluation is a key technology to be considered in the design of multiple aircrafts formation(MAF)configurations with high dynamic properties in engineering applications.This paper deduces the relationship between relative velocity,dynamic safety distance and dynamic adjacent distance of formation members,then divides the formation states into collision-state and matching-state.Meanwhile,probability models are constructed based on the binary normal distribution of relative distance and relative velocity.Moreover,configuration evaluation strategies are studied by quantitatively analyzing the denseness and the basic capabilities according to the MAF collision-state probability and the MAF matching-state probability,respectively.The scale of MAF is grouped into 5 levels,and previous lattice-type structures are extended into four degrees by taking the relative velocities into account to instruct the configuration design under complex task conditions.Finally,hardware-in-loop(HIL)simulation and outfield flight test results are presented to verify the feasibility of these evaluation strategies.

On Conditional Probabilities of Factoring Quadratics

Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.

Analysis of video head impulse test saccades data in patients with vestibular migraine or probable vestibular migraine

Objective:Saccades accompanied by normal gain in video head impulse tests(vHIT)are often observed in patients with vestibular migraine(VM).However,they are not considered as an independent indicator,reducing their utility in diagnosing VM.To better understand clinical features of VM,it is necessary to understand raw saccades data.Methods:Fourteen patients with confirmed VM,45 patients with probable VM(p-VM)and 14 agematched healthy volunteers were included in this study.Clinical findings related to spontaneous nystagmus(SN),positional nystagmus(PN),head-shaking nystagmus(HSN),caloric test and vHIT were recorded.Raw saccades data were exported and numbered by their sequences,and their features analyzed.Results:VM patients showed no SN,PN or HSN,and less than half of them showed unilateral weakness(UW)on caloric test.The first saccades from lateral semicircular canal stimulation were the most predominant for both left and right sides.Neither velocity nor time parameters were significantly different when compared between the two sides.Most VM patients(86%)exhibited small saccades,around 35%of the head peak velocity,with a latency of 200e400 ms.Characteristics of saccades were similar in patients with p-VM.Only four normal subjects showed saccades,all unilateral and seemingly random.Conclusions:Small saccades involving bilateral semicircular canals with a scattered distribution pattern are common in patients with VM and p-VM.