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.

X and γ-rays emission probabilities of ^(131)I and ^(133)Xe

Radioactive nuclides as 131I and 133Xe are increasingly used for both clinical diagnosis and therapeutic treatment of the patient. For example, 131I is used for the treatment of thyroid gland cancer. Otherwise, 133Xe is used in ventilation studies to assess and evaluate pulmonary function and to provide images of the lungs in both cardiac and pulmonary diseases, such as asthma, pulmonary emphysema, bronchiectasis, carcinoma of the lung, and pulmonary embolism [1,2]. Furthermore, cerebral blood flow is measured using 133Xe inhalation. In this study, the X and γ-rays emission probabilities in the decay of 131I and 133Xe were precisely measured with a calibrated Si(Li) detector. Results of this study were compared using available results in the literature. Good agreement was observed between our results and available results in the literature.

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.

Robust analysis of discounted Markov decision processes with uncertain transition probabilities

Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.

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.

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.

HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS

In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.

A General Model for Hepatitis B Disease with Age-Dependent Susceptibility and Transmission Probabilities

A SEI model for hepatitis B is constructed where the susceptibility and other crucial transmission probabilities depend on the chronological age and the basic reproduction rate R0 is derived. Under suitable (biological and mathematical) assumptions in a closed population, results of Houpa D. D. E. et al. [1] are extended from constant case of p and q to age-dependent case: the disease-free equilibrium is globally asymptotically stable (GAS) if R0 . On the other hand, R0 > 1 induces that endemic equilibrium is GAS and the system is uniformly persistent.

Variable structure control for descriptor Markovian jump systems subject to partially unknown transition probabilities

The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.

Assessing Probabilities of Unique Events in Decision Making

This paper outlines a two-stage assessment procedure for deriving probabilities of unique events.The calculations are illustrated using possible events pertaining to the Lehman failure in 2008.The procedures utilize pairwise comparisons associated with the Analytic Hierarchy Process.Typical betting odds are used to motivate an ordering of qualitative judgments that are then converted into quantitative assessments and finally a probability distribution.

Assessing Probabilities of Unique Events: A New Approach

Decision-makers in unique or one-off situations may have difficulties in framing the probabilities of possible events that are required in modern decision-making. This paper illustrates a new approach to probability determination based on pairwise primary judgments on the relative likelihoods of the possible events. Related “news” on the situation can also be used to update these prior probabilities using Bayesian Revision. Illustrative calculations outline the entire process through to determination of posterior probabilities following a “news” event.

Comparison of Ruin Probabilities in Compound Poisson Risk Model

Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

Energy Levels, Oscillator Strengths, and Transition Probabilities of Ni XIX and Cu XX

Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relativistic effects are considered. The calculations are compared with other results in the literature. A good agreement is found. We also report on some unpublished energy values.

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.

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.

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.

Theoretical Calculations of Transition Probabilities and Oscillator Strengths for Sc（Ⅲ） and Y（Ⅲ）

The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc（Ⅲ） and Y（Ⅲ）. In this method, by solving the SchrSdinger equation of the weakest bound electron, the expressions of energy eigenvalue and the radial function can be obtained. And a coupled equation is used to determine the parameters which are needed in the calculations. The ob- tained results of Sc（III） from this work agree very well with the accepted values taken from the National Institute of Standards and Technoligy （NIST） data base, most deviations are within the accepted level. For Y（Ⅲ） there are no accepted values reported by the NIST data base. So we compared our results of Y（Ⅲ） with other theoretical results, good agreement is also obtained.

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）.

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.