Upper bounds for ruin probabilities under model uncertainty

Abstract

In this paper, we investigate some ruin problems for risk models that contain uncertainties on both claim frequency and claim size distribution. The problems naturally lead to the evaluation of ruin probabilities under the so-called G-expectation framework. We assume that the risk process is described as a class of G-compound Poisson process, a special case of the G-Lévy process. By using the exponential martingale approach, we obtain the upper bounds for the two-sided ruin probability as well as the ruin probability involving investment. Furthermore, we derive the optimal investment strategy under the criterion of minimizing this upper bound. Finally, we conclude that the upper bound in the case with investment is less than or equal to the case without investment.     

Risk minimization for an insurer with investment and reinsurance via g-expectation

Abstract

This paper is devoted to the study of a risk-based optimal investment and proportional reinsurance problem. The surplus process of the insurer and the risky asset process in the financial market are assumed to be general jump-diffusion processes. We use a convex risk measure generated by g-expectation to describe the risk of the terminal wealth with investment and reinsurance. Under the aim of minimizing the risk, the problem is solved by using techniques of stochastic maximum principles. Two interesting special cases are studied and the explicit expressions for optimal strategies and corresponding minimal risks are derived.     

Optimal control strategies for dividend payments and capital injections in compound Markov binomial risk model with penalties for deficits

We consider the compound Markov binomial risk model. The company controls the amount of dividends paid to the shareholders as well as the capital injections in order to maximize the cumulative expected discounted dividends minus the discounted capital injections and the discounted penalties for deficits prior to ruin. We show that the optimal value function is the unique solution of an HJB equation, and the optimal control strategy is a two-barriers strategy given the current state of the Markov chain. We obtain some properties of the optimal strategy and the optimal condition for ruining the company. We offer a high-efficiency algorithm for obtaining the optimal strategy and the optimal value function. In addition, we also discuss the optimal control problem under a restriction of bounded dividend rates. Numerical results are provided to illustrate the algorithm and the impact of the penalties.     

Optimization problems for consecutive-2-out-of-n:G system

Abstract

This paper considers the optimization problems for a consecutive-2-out-of-n:G system where n is considered to be fixed or random. When the number of components is constant, the optimal number of components and the optimal replacement time are discussed by minimizing the expected cost rates. Furthermore, we focus on the above discussions again when n is a random variable. We give an approximate value of MTTF and propose the preventive replacement policy, respectively.     

Time series models associated with Mittag-Leffler type distributions and its properties

ABSTRACT

We have provided a fractional generalization of the Poisson renewal processes by replacing the first time derivative in the relaxation equation of the survival probability by a fractional derivative of order α(0 < α ? 1). A generalized Laplacian model associated with the Mittag-Leffler distribution is examined. We also discuss some properties of this new model and its relevance to time series. Distribution of gliding sums, regression behaviors, and sample path properties are studied. Finally we introduce the q-Mittag-Leffler process associated with the q-Mittag-Leffler distribution.     

Optimal investment strategy for a DC pension plan with mispricing under the Heston model

Abstract

In this article, we consider the optimal investment problem for a defined contribution (DC) pension plan with mispricing. We assume that the pension funds are allowed to invest in a risk-free asset, a market index, and a risky asset with mispricing, i.e. the prices are inconsistent in different financial markets. Assuming that the price process of the risky asset follows the Heston model, the manager of the pension fund aims to maximize the expected utility for the power utility function of terminal wealth. By applying stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman (HJB) equation. And the optimal investment strategy is obtained for the power utility function explicitly. Finally, numerical examples are provided to analyze effects of parameters on the optimal strategy.     

On the Parameter Estimation of the Asymmetric Multivariate Laplace Distribution

This article examines a family of three-parameter multivariate Laplace distributions ML _p (a, μ, Σ) which is closed under constant shifts. Parameter vectors a and μ are called shift and shape parameter, respectively, positive definite p × p-matrix Σ is a scale parameter. The first three moments are derived and used for estimating the parameters. The behavior of the obtained estimates is explored in a simulation experiment.     

Local rates of convergence for consistent estimators of location of translation families

We consider the estimation of a location parameter θ in a one-sample problem. A measure of the asymptotic performance of an estimator sequence {T_n} = T is given by the exponential rate of convergence to zero of the tail probability, which for consistent estimator sequences is bounded by a constant, B (θ, ?), called the Bahadur bound. We consider two consistent estimators: the maximum-likelihood estimator (mle) and a consistent estimator based on a likelihood-ratio statistic, which we call the probability-ratio estimator (pre). In order to compare the local behaviour of these estimators, we obtain Taylor series expansions in ? for B (θ, ?) and the exponential rates of the mle and pre. Finally, some numerical work is presented in which we consider a variety of underlying distributions.     

Ohio Little Magazines

Abstract

The company now known as DC began as National Periodicals, publishing anthology series such as Adventure Comics, More Fun Comics, and Detective Comics. Superman, the first true “super-hero,” appeared on the scene in a brief story in Action Comics no. 1 (June, 1938). Batman appeared not long after, in the pages of Detective Comics no. 27 (May 1939)|3-and the world was never the same. In the late 1940s, National absorbed its competitor Ail-American Comics (which published such series as Green Lantern, Aquaman, and Green Arrow) and changed the company's name to Detective Comics, “DC” for short. The merger made DC the largest comic book company until the 1950s, when interest in the medium dried up, and Dell, who at that time published Walt Disney's comic books, took over the top spot.     

Consistency of stochastic approximation algorithm with quasi-associated random errors

ABSTRACT

Many mathematical and physical problems are led to find a root of a real function f. This kind of equation is an inverse problem and it is difficult to solve it. Especially in engineering sciences, the analytical expression of the function f is unknown to the experimenter, but it can be measured at each point x_k with M(x_k) as expected value and induced error ξ_k. The aim is to approximate the unique root θ under some assumptions on the function f and errors ξ_k. We use a stochastic approximation algorithm that constructs a sequence (x_k)_{k ? 1}. We establish the almost complete convergence of the sequence (x_k)_k to the exact root θ by considering the errors (ξ_k)_k quasi-associated and we illustrate the method by numerical examples to show its efficiency.     

A Statistical Model for Shelf Life Estimation Using Sensory Evaluations Scores

Abstract

This article focuses on the problem of estimating the shelf life of food products by modeling the results coming from sensory evaluations. In such studies, trained panelists are asked to judge food attributes by reference to a scale of numbers (scores varying often from 0 to 6). The usual statistical approach for data analysis is to fit a regression line relating the scores and the time of evaluation. The estimate of the shelf life is obtained by solving the regression equation and replacing the score by a cut-off point (which indicates product “failure”) previously chosen by the food company. The procedure used in these sensory evaluations is such that one never knows the exact “time to failure”. Consequently, data arising from these studies are either right or left censored. We propose a model which incorporates these informations and assumes a Weibull for the underlying distribution of the failure time. Simulation studies were implemented. The approach was used in a real data set coming from sensory evaluations of a dehydrated food product.     

EBSCO Publishing

Abstract

EBSCO Publishing is an innovative company that has its roots in paper publishing. It now produces hundreds of online resources in a state-of-the-art facility located along the banks of the Ipswich River in Massachusetts. Considerable work occurs behind the scenes in Ipswich (and around the world) to produce the online databases in EBSCOhost that appear to the user at the click of a mouse. Jennifer Carroll toured the headquarters in Ipswich to learn about the processes that make these valuable resources available.     

Order-preserving Estimators and an Inequality on the Integration of Zonal Polynomial

ABSTRACT

Suppose X , p × p p.d. random matrix, has the distribution which depends on a p × p p.d. parameter matrix Σ and this distribution is orthogonally invariant. The orthogonally invariant estimator of Σ which has the eigenvalues of the same order as the eigenvalues of X is called order-preserving. We conjecture that a non-order-preserving estimator is dominated by modified order-preserving estimators with respect to the entropy (Stein's) loss function. We show that an inequality on the integration of zonal polynomial is sufficient for this conjecture. We also prove this inequality for the case p = 2.     

Equilibrium strategies in a constant retrial queue with setup time and the N-policy

Abstract

In this article, customers’ strategic behavior and social optimation in a constant retrial queue with setup time and the N-policy are investigated. Customers who find the server isn’t idle either leave forever or enter an orbit. After a service, the server will seek a customer from the orbit at a constant rate. The server is closed whenever the system becomes empty, and is activated when the number of waitlisted customers reaches a threshold. We obtain the equilibrium arrival rates in different states. There exist both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors. Through the Particle Swarm Optimization (PSO) algorithm, we numerically obtain the optimal solution of the social welfare maximization problem. Finally, numerical examples are presented to illustrate the sensitivity of system performance measures.     

A NOTE ON ESTIMATING LINEAR TREND IN A REGRESSION MODEL WITH SERIALLY CORRELATED ERROR COMPONENTS

ABSTRACT

We consider a linear trend regression model when the disturbances follow a serially correlated one-way error component model. In this model, we investigate the performance of the Ordinary Least Squares Esitmator (OLSE), First Difference Estimator (FDE), Generalized Least Squares Estimator (GLSE) and the Cochrane-Orcutt-Transformation Estimator (COTE) of slope coefficient in terms of efficiency. The main findings are as follows: (1) when the autocorrelation is close to unity, then the FDE is approximately the GLSE; (2) the OLSE is better than the COTE; and (3) when the value of the autocorrelation is kept constant and T → ∞, the OLSE, COTE and GLSE are asymptotically equivalent whereas the FDE is worse than the other estimators in terms of efficiency.     

A Resampling Approach for Under-estimating a Finite Population Total from a Censored Sample

Abstract

Suppose a finite population of N objects each of which has an unknown value μ _i  ≥ 0, i = 1, … , N of a nonnegative characteristic of interest. A random sample has been drawn, but only for a selected subset of the sample the μ-values have been observed. The subset selection procedure has been somewhat obscure, and thus the subsample is censorized rather than random. Despite that, a reliable lower bound for the population total (the sum of all μ _i ) is required which uses the statistical information contained in the data. We propose a resampling procedure to construct an under-estimate of the population total. We also consider the case when the objects of the population have unequal sampling probabilities, in particular when the population is divided into a few number of strata with constant probabilities within each stratum. A real data example illustrates the method.     

Culinary Magazines

Abstract

Marvel Comics, along with rival DC Comics, is one of the two powerhouses of the comic book industry and has been for many decades. The company was founded in 1939 by pulp magazine publisher Martin Goodman. Goodman owned various publishing houses responsible for a variety of pulp titles, including Marvel Science Stories. In 1939, a colleague persuaded Goodman that comic books were the upcoming trend in periodical publishing, so Good-man launched a book called Marvel Comics. Issue no. 1 contained a story by Bill Everett about the Sub-Mariner, as well as the first appearance of the Human Torch. Both characters quickly became leading draws of the Golden Age of comics. Soon after, Goodman hired writer Joe Simon and artist Jack Kirby, who were to become giants in the industry. Simon and Kirby created Captain America, a character who remains a comics icon even today. In those early days, Goodman also hired another future legend: writer Stan Lee, who happened to be Good-man's nephew.

Goodman's comic company was known officially as Timely Comics, Inc., then later as Atlas Publishing. The firm did not change its name to Marvel until the early 1960s. Timely benefitted from the comics boom of the early 1940s, but interest in super-hero stories waned later in the decade. Atlas briefly revived its super-hero line-up in 1954, but the company spent most of the next decade publishing romance, western, horror, and humor comics.1 1. Les Daniels, Marvel: Five Decades of the World's Greatest Comics (NY: Abrams, 1991), pp. 17–23, 26–36, 40–61.¹     

Partly linear models on Riemannian manifolds

In partly linear models, the dependence of the response y on (x ^T, t) is modeled through the relationship y=x ^T β+g(t)+?, where ? is independent of (x ^T, t). We are interested in developing an estimation procedure that allows us to combine the flexibility of the partly linear models, studied by several authors, but including some variables that belong to a non-Euclidean space. The motivating application of this paper deals with the explanation of the atmospheric SO₂ pollution incidents using these models when some of the predictive variables belong in a cylinder. In this paper, the estimators of β and g are constructed when the explanatory variables t take values on a Riemannian manifold and the asymptotic properties of the proposed estimators are obtained under suitable conditions. We illustrate the use of this estimation approach using an environmental data set and we explore the performance of the estimators through a simulation study.     

Methods for calculating stationary distribution in linear models of time series

The article deals with methods for computing the stationary marginal distribution in linear models of time series. Two approaches are described. First, an algorithm based on approximation of solution of the corresponding integral equation is briefly reviewed. Then, we study the limit behaviour of the partial sums c ₁ η₁+c ₂ η₂+···+c _n η _n where η _i are i.i.d. random variables and c _i real constants. We generalize procedure of Haiman (1998) [Haiman, G., 1998, Upper and lower bounds for the tail of the invariant distribution of some AR(1) processes. Asymptotic Methods in Probability and Statistics, 45, 723–730.] to an arbitrary causal linear process and relax the assumptions of his result significantly. This is achieved by investigating the properties of convolution of densities.