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421.
D. Kuang 《Scandinavian actuarial journal》2020,2020(6):553-576
ABSTRACT We propose an asymptotic theory for distribution forecasting from the log-normal chain-ladder model. The theory overcomes the difficulty of convoluting log-normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder-based bootstrap. We embed the log-normal chain-ladder model in a class of infinitely divisible distributions called the generalized log-normal chain-ladder model. The asymptotic theory uses small σ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application. 相似文献
422.
In this paper, we study the classical problem of the first hitting time density to a moving boundary for a diffusion process, which satisfies the Cherkasov condition, and hence, can be reduced to a standard Wiener process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for both. By using the method of heat potentials, we show how to reduce these problems to linear Volterra integral equations of the second kind. For small values of t, we solve these equations analytically by using Abel equation approximation; for larger t we solve them numerically. We illustrate our method with representative examples, including Ornstein–Uhlenbeck processes with both constant and time-dependent coefficients. We provide a comparison with other known methods for finding the hitting density of interest, and argue that our method has considerable advantages and provides additional valuable insights. We also show applications of the problem and our method in various areas of financial mathematics. 相似文献
423.
Abstract A displaced Poisson process is presented as a reasonable model in describing the stages of certain chronic diseases. Although in some respects the model is an oversimplification of the true picture its feature is that it facilitates the easy estimation of some of the important parameters that arise in this area. Among the quantities estimated are the mean lead time and the distribution function of the time spent in the preclinical state. Properties of some of the estimators are obtained. 相似文献
424.
Nader Ebrahimi 《Metrika》1993,40(1):339-348
The role of the so-called surplus processes in the assessment of probability of survival of a company is well-known in risk theory and applications thereof. However, the insurance models used in this regard ignore the fact that, in many situations, no relevant information is available for the assessment of survival after the company goes out of business. In this paper, we revisit the classical risk model in order to remedy this situation. Having stopped the deficit process, which is negative of the surplus process, at the time of ruin, under two different sampling schemes, we obtain inference procedure for ruin probabilities. As by products of our methodology, we also obtain procedures to assess the reliability of systems whose survival depends on a cumulative damage process, which is equivalent to the aggregate claim size process of the classical risk model. 相似文献
425.
This paper presents a first model integrating the relation between biodiversity loss and zoonotic pandemic risks in a general equilibrium dynamic economic set-up. The occurrence of pandemics is modeled as Poissonian leaps in economic variables. The planner can intervene in the economic and epidemiological dynamics in two ways: first (prevention), by deciding to conserve a greater quantity of biodiversity to decrease the probability of a pandemic occurring, and second (mitigation), by reducing the death toll through a lockdown policy, with the collateral effect of affecting negatively labor productivity. The policy is evaluated using a social welfare function embodying society’s risk aversion, aversion to fluctuations, degree of impatience and altruism towards future generations. The model is explicitly solved and the optimal policy described. The dependence of the optimal policy on natural, productivity and preference parameters is discussed. In particular the optimal lockdown is more severe in societies valuing more human life, and the optimal biodiversity conservation is larger for more “forward looking” societies, with a small discount rate and a high degree of altruism towards future generations. Moreover, societies accepting a large welfare loss to mitigate the pandemics are also societies doing a lot of prevention. After calibrating the model with COVID-19 pandemic data we compare the mitigation efforts predicted by the model with those of the recent literature and we study the optimal prevention–mitigation policy mix. 相似文献
426.
Let ( Xn , n ≥ 1) be an i.i.d. sequence of positive random variables with distribution function H . Let φ H := {(n, Xn ), n ≥ 1) be the associated observation process. We view φ h as a measure on E := [0, ∞) ∞ (0, φ] where φH (A) is the number of points of φ H which lie in A . A family ( Vs , s> 0) of transformations is defined on E in such a way that for suitable H the distributions of ( Vs φH , S > 0) satisfy a large deviation principle and that a related Strassen-type law of the iterated logarithm also holds. Some consequent large deviation principles and loglog laws are derived for extreme values. Similar results are proved for φ H replaced by certain planar Poisson processes. 相似文献
427.
The purchase behaviour of consumers is observed in a panel during a month. The quantity of interest is the penetration of a product. The problem is that this quantity has to be estimated on the basis of incomplete data. For some or all respondents some weeks are missing. To this end the purchasing process is modeled with a variety of stochastic processes. The performance of some existing models is compared for penetrations of the complete population, but also for Bayesian estimates in subpopulations. 相似文献
428.
This paper develops semiparametric Bayesian estimation approach for Poisson regression models with unobserved heterogeneity of unknown density. This approach is computationally efficient and allows automatic adaptation of the approximating density to data during estimation. Simulations show the estimator performs well. 相似文献
429.
This paper provides evidence on the role of sunk costs in the market expansion of continuing exporters, explicitly accounting for the number of target export destinations. We use dynamic count data models to address the discrete non‐negative nature and skewed distribution of the dependent variable, the number of export markets. By examining the trade patterns of individual firms, we find that past export market coverage significantly improves the ability of Ukrainian exporters for further expansion. The results also indicate that information spillovers from neighbouring firms and foreign ownership are not important factors for the market expansion of incumbent exporters. 相似文献
430.
Abstract A new and very simple test for uniformity is proposed. An exact formula for the distribution under H0 of the corresponding test statistic is derived. This formula is only suitable for computer-oriented use. For other circumstances a table of critical values is given. The power of the test is compared with that of two well-known alternatives: the χ2 -test and the Kolmogorov-Smirnov test. 相似文献