Compound Mixed Poisson Distributions II

Market cycles play a great role in reinsurance. Cycle transitions are not independent from the claim arrival process: a large claim or a high number of claims may accelerate cycle transitions. To take this into account, a semi-Markovian risk model is proposed and analyzed. A refined Erlangization method is developed to compute the finite-time ruin probability of a reinsurance company. Numerical applications and comparisons to results obtained from simulation methods are given. The impact of dependency between claim amounts and phase changes is studied.     

On the severity of ruin in a Markov-modulated risk model

We consider a Markov-modulated risk model in which the claim inter-arrivals, amounts and premiums are influenced by an external Markovian environment process. A system of Laplace transforms of the probabilities of the severity of ruin, given the initial environment state, is established from a system of integro-differential equations derived by Snoussi [The severity of ruin in Markov-modulated risk models Schweiz Aktuarver. Mitt., 2002, 1, 31–43]. In the two-state model, explicit formulas for probabilities of the severity of ruin are derived, when the initial reserve is zero or when both claim amount distributions are from the rational family. Numerical illustrations are also given.     

A. Palmström

Abstract

1. Mr R. Frisch has recently ¹ Ragnar Frisch: Sur les semi-invariants et moments employés dans l'étude des distributions statistiques, Oslo, 1926 (Det Norske VidenskabsAkademis Skrifter, II N:o 3), p. 26. established the interesting identity     

Seasonal mortality for fractional ages in short term life insurance

Abstract

Fernández-Durán, and Gregorio-Domínguez, Seasonal Mortality for Fractional Ages in Life Insurance. Scandinavian Actuarial Journal. A uniform distribution of deaths between integral ages is a widely used assumption for estimating future-lifetimes; however, this assumption does not necessarily reflect the true distribution of deaths throughout the year. We propose the use of a seasonal mortality assumption for estimating the distribution of future-lifetimes between integral ages: this assumption accounts for the number of deaths that occurs in given months of the year, including the excess mortality that is observed in winter months. The impact of this seasonal mortality assumption on short-term life insurance premium calculations is then examined by applying the proposed assumption to Mexican mortality data.     

Research productivity patterns in the organizational behavior and human resource management literature

Closely following the analysis approach used for similar studies in the economics and finance literature, we present the first study to examine if there exists an empirical regularity in the bibliometric patterns of research productivity in the organizational behavior (OB) and human resource management (HRM) literature. Our results present strong evidence that there indeed exists a distinct empirical regularity. It is the so-called Generalized Lotka's Law of scientific productivity pattern: The number of authors publishing n papers is about 1/n^c of those publishing one paper. The observed pattern in the OB and HRM area is interestingly very consistent with those in much older, related business disciplines.     

One-step R-estimation in linear models with stable errors

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α$\alpha$-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators remain root-n$n$ consistent (the optimal rate) under the whole family of stable distributions, irrespective of their asymmetry and tail index. While parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (_α0,_b0)$({\alpha }_0,b_0)$ of the tail index α$\alpha$ and skewness parameter b$b$, while preserving root-n$n$ consistency under any (α,b)$(\alpha ,b)$ as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.     

Asymptotic properties of MLE and UMVUE in one-parameter truncated distributions

Consider one-parameter families of continuous distributions whose range depend on an unknown parameter. In case a single sufficient and complete statistic exists, we obtain the limiting distributions of MLE and UMVUE. Both distributions are different transformations of a standard exponential variable.     

Multivariate stable ARMA processes with time dependent coefficients

This paper considers the class of m-variate autoregressive moving average (ARMA) processes with stable innovations and time dependent coefficients. A set of suitable AR and MA regularity conditions is given to ensure existence and uniqueness of valid solutions. A simple form of the above solution is expressed in terms of one sided Green's matrix functions associated with the AR operator. We solve the prediction problem arising in this class of models. A few examples are added to support the general theory.     

Uncertainty and the size distribution of rewards from innovation

 Previous research has shown that the distribution of profit outcomes from technological innovations is highly skew. This paper builds upon those detailed findings to ask: what stochastic processes can plausibly be inferred to have generated the observed distributions? After reviewing the evidence, this paper reports on several stochastic model simulations, including a pure Gibrat random walk with monthly changes approximating those observed for high-technology startup company stocks and a more richly specified model blending internal and external market uncertainties. The most highly specified simulations suggest that the set of profit potentials tapped by innovators is itself skew-distributed and that the number of entrants into innovation races is more likely to be independent of market size than stochastically dependent upon it.     

湖北省油菜保险纯费率比较研究——基于不同单产分布下的实证研究

在农作物保险费率厘定当中,期望损失是影响纯费率准确性的关键因素,因此在不同的产量分布下会出现不同的纯费率,本文使用四种参数方法与一种非参数方法,共五种分布对湖北省78个县市①的油菜单产保险纯费率进行厘定,发现不同分布下厘定的费率明显不同,并采取定性与定量相结合的方法对五种分布拟合的效果做出评价。