Probability of ruin of an insurance company for the poisson model

The probability of ruin of an insurance company over an infinite interval and the conditional average time before the ruin of the insurance company for the Poisson flows of insurance premiums and payments are found. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 28–33, April, 1999.     

Calculation of the Probability of Survival of an Insurance Company with Allowance for the Rate of Return for a Poisson Stream of Premiums

The probability of survival of an insurance company with the working capital is calculated for a Poisson stream of premiums.     

Default risk modeling with position-dependent killing

Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One “stylized fact” is fundamental for our consideration: empirically default is a rather rare event, especially in the investment grade categories of credit ratings. Hence, the action of killing may be considered as a small parameter. In a number of special cases we derive closed-form expressions for the entire term structure of the cumulative probability of default, its hazard rate, and intensity. Comparison with historical data on aggregate global corporate defaults confirms the validity of the perturbation method for estimations of long-term probability of default for companies with high credit quality. On a single company level, we implement the derived formulas to estimate the one-year likelihood of default of Enron on a daily basis from August 2000 to August 2001, three months before its default, and compare the obtained results with forecasts of traditional structural models.     

The effects of tilt corrected residual aberration on the detection probability of single-photon propagation in a slant path turbulent atmosphere

Based on the assumption of a pulse laser beam with an initial Gaussian temporal shape and a collimated fundamental-model Gaussian beam, the Rytov approximation and Kolmogorov spectrum model for the index-of-refraction fluctuation of atmosphere, the effect of turbulence on the probability density, acquisition transmittance probability, transmittance probability density, acquisition probability of single-photon propagation in atmospheric communication channel with z-tilt and centroid-tilt aberration corrected are studied theoretically. The probability density, acquisition transmittance probability, transmittance probability density and acquisition probability models for single-photon propagation in uplink path and downlink path are derived. Our results shown that the detection probability and the acquisition transmittance probability of the single-photon are obvious increase, when the beams are propagation in the z-tilt corrected communication channel.     

Geographical dispersal of mobile communication networks

In this paper, we analyze statistical properties of a communication network constructed from the records of a mobile phone company. The network consists of 2.5 million customers that have placed 810 million communications (phone calls and text messages) over a period of 6 months and for whom we have geographical home localization information. It is shown that the degree distribution in this network has a power-law degree distribution k⁻⁵ and that the probability that two customers are connected by a link follows a gravity model, i.e. decreases as d⁻², where d is the distance between the customers. We also consider the geographical extension of communication triangles and we show that communication triangles are not only composed of geographically adjacent nodes but that they may extend over large distances. This last property is not captured by the existing models of geographical networks and in a last section we propose a new model that reproduces the observed property. Our model, which is based on the migration and on the local adaptation of agents, is then studied analytically and the resulting predictions are confirmed by computer simulations.     

Mathematical Model of Functioning of an Insurance Company with Allowance for Advertising Expenses

A mathematical model of the functioning of an insurance company with allowance for advertising expenses is suggested. The basic characteristics of the capital of the company and the advertising efficiency are examined in the case in which the advertising expenses are proportional to the capital.     

Zipf's law in income distribution of companies

Distribution functions of annual income of companies are analyzed based on two company databases. A clear power law distribution consistent with the Zipf's law can be confirmed for Japanese companies over more than three decades in income scale. Similar distributions can be confirmed in some other countries. It is confirmed that such power laws hold in most of job categories with slightly modified exponents. An annual income of a company is about two orders of magnitude smaller than its total assets, and the growth rate distribution of income is nearly independent of the income size in contrast to the case of growth rate of assets.     

Model of functioning of an insurance company with a finite number of potential clients

A model of the functioning of an insurance company is suggested, when the number of potential clients is finite, and the basic characteristics of the number of clients and the capital of the company are studied in the stationary regime. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–39, April, 1999.     

Probability distributions for the overlaps and self-correlations of the pure states of ann-vector model

The probability distributions for the overlaps between and the self-correlations of the pure states of the Stanleyn-vector model with infinite-range interactions are derived. These probability distributions represent two new order parameters for the model and are intimately related to the parameters which arise naturally within the replica formalism for the treatment of the corresponding quenched random-bond model. In contrast to then = 1 Ising case, the probability distributions are nontrivial whenn > 1 and an additional parameter for self-correlation has to be introduced.     

An absolute measurement of the probability for 1s σ and 2p σ excitation of the leadK shell

Using particle x-ray coincidence techniques, the probability forK shell ionization has been measured absolutely at two impact parameters for collisions of 5.8 MeV/amu²⁰⁸Pb on Ag and Au. In the asymmetric collision system Pb-Ag, the 1sσ excitation probability of the PbK shell is 2.2% at 25 fm impact parameter, and an exponential probability distribution falls off too quickly to account for the measured total cross section. For the symmetric system Pb-Au, the latter conclusion is also made for the 2pσ excitation probability although in this case, the probability is much larger being 29% at 42 fm.     

Nonstandard (non-σ-additive) probabilities in algebraic quantum field theory

Traditionally, physicists deduce the observational (physical) meaning of probabilistic predictions from the implicit assumption that thewell-defined events whose probabilities are 0 never occur. For example, the conclusion that in a potentially infinite sequence of identical experiments with probability 0.5 (like coin tossing) the frequency of heads tends to 0.5 follows from the theorem that sequences for which the frequencies do not tend to 0.5 occur with probability 0. Similarly, the conclusion that in quantum mechanics, measuring a quantity always results in a number from its spectrum is justified by the fact that the probability of getting a number outside the spectrum is 0. In the mid-60s, a consistent formalization of this assumption was proposed by Kolmogorov and Martin-Löf, who defined arandom element of a probability space as an element that does not belong to any definable set of probability 0 (definable in some reasonable sense). This formalization is based on the fact that traditional probability measures are σ-additive, i.e., that the union of countably many sets of probability 0 has measure 0. In quantum mechanics with infinitely many degrees of freedom (e.g., in quantum field theory) and in statistical physics one must often consider non-σ-additive measures, for which the Martin-Löf's definition does not apply. Many such measures can be defined as “limits” of standard probability distributions. In this paper, we formalize the notion of a random element for such finitely-additive probability measures, and thus explain the observational (physical) meaning of such probabilities.     

Doppler-Rabi oscillations of a two-level atom moving in a cavity

The interaction with a quantum mode of a high-Q cavity is considered for a two-level atom uniformly moving along the classical trajectory. The method of dressed states is employed to deduce the recursion relation for the probability of atomic transition with photon emission. It is shown that the dependence of the transition probability on the position of a moving atom in the cavity and the magnitude of this probability are qualitatively influenced by the ratio between the Doppler shift of transition frequency and the Rabi frequency of atom-field system.     

Symmetric semistable measures on Rn and symmetric semistable distribution operators in quantum mechanics

The paper contains two theorems. The first one deals with the classic probability, provides the form of the characteristic function of a symmetric, semistable probability distribution in Rⁿ. By a semistable probability distribution we mean a certain class of limit distributions of the sequence of random variables, containing the classic stable probability distribution and included in a set of infinitely divisible distributions.The result will be applied in the proof of the second theorem on non-commutative probability, in which we deal with the generalization of the central limit theorem in quantum mechanics.In the paper we define the symmetric semistable probability distributions for pairs of canonical observables in a state ?₀. In the second theorem we indicate that the symmetric semistable distribution operator is a ground state. By a ground state we mean a state for which Heisenberg's inequality becomes an equality.     

Capability of markets to accept a new stock

Privatization is one of the most important elements of the continuing global phenomenon of the increasing use of markets to allocate resources. One important motivation for privatization is to help develop factor and product markets, as well as security markets. Among the various factors of market development, we try to answer to one of the main question: ‘which group of markets or indices is better to develop and absorb a new company?’. Our method is based on Level Crossing to quantify the following factors: stage of development, activity and risk of indices. As an example, considering Tehran Price Index (TEPIX), we compare financial and industrial indices to find which index is more preferable to absorb a new company in its group.     

工业X射线机的射束均匀性检验

在与法国某公司的合作项目中,对射线机的性能做了充分的评估,针对工业X射线机射束均匀性的检验给出了实验内容、过程和结果分析。实验所用射线机分别为ISOVOLT320/13与XYD-225/10,两台设备的实验结果均符合该公司质控文件规定,满足黑度差不超过0.3的要求。定期对射线机进行射束均匀性检验,将有利于监测射线机的工作状态,以保证检测工作的准确性和一致性。     

Nature of Nonlocality in Triangle Network based on Elegant Joint Measurement

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in [Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In [npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, it finds the nature of the correlation in a triangle network scenario. This study observes how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here, it uses the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. It also checks the probability bound for the polygon structure.     

Probability of fade for airborne laser communication system over exponentiated Weibull distribution under aperture averaging

In this paper, the probability of fade is performed for the airborne laser communication systems considering both the atmospheric and aero-optic effects. The atmospheric fluctuation is characterized by the exponentiated Weibull (EW) fading channel. The novel analytical expression is derived for probability of fade according to Meijer’s G function. The probability of fade is demonstrated to the simulation data with the Gamma–Gamma and log-normal distributions. The probability of fade is obtained for different flight altitudes and propagation distances. The probability of fade is analyzed in the airborne laser communication systems under the effect of aperture averaging in weak-to-strong turbulence regime. Results suggest that the proposed EW model is valid in airborne laser communication with high altitude, especially in the lower values of the irradiance under atmospheric turbulence and aero-optics effect. The fading of outage performance can be effectively mitigated by aperture averaging. Furthermore, this work is helpful for the compensate technique of system performance on airborne optical communication system.     

开放边界条件下平面环行交叉路口交通流的相图研究

运用具有内、外环车道的平面环形交叉路口元胞自动机模型,对开放边界条件下平面环行交叉路口的交通流进行研究.计算机模拟结果表明:边界条件和道路瓶颈影响着平面环形交叉路口交通流的性质,产生概率和消失概率均只在一定范围内影响系统流量的变化.根据系统流量与产生概率和消失概率的关系,将系统分为三个相区,并对相图进行研究,为实际交通控制提供参考.     

Probability and complex quantum trajectories: Finding the missing links

It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that defined a conserved probability for most of the regions in the complex space in terms of a trajectory integral, indicating a dynamical origin of quantum probability. There it was also shown that the quantum trajectories obtained are the same characteristic curves that propagate information about the conserved probability density. Though the probability density we now adopt for those regions left out in the previous work is not conserved locally, the net source of probability for such regions is seen to be zero in the example considered, allowing to make the total probability conserved. The new combined probability density agrees with the Born’s probability everywhere on the real line, as required. A major fall out of the present scheme is that it explains why in the classical limit the imaginary parts of trajectories are not observed even indirectly and particles are confined close to the real line.