In this article, we provide an estimation and several asymptotic behaviors for the coherent entropic risk measure of compound Poisson process. We also establish an estimation for the coherent entropic risk measure of sum of i.i.d. random variables in virtue of Log-Sobolev inequality. As an...

We consider in this paper that the reserve of an insurance company follows the classical model, in which the aggregate claim amount follows a compound Poisson process. Our goal is to minimize the ruin probability of the company assuming that the management can invest dynamically part of the...

This paper studies likelihood-based estimation and inference in parametric discontinuous threshold regression models with i.i.d. data. The setup allows heteroskedasticity and threshold effects in both mean and variance. By interpreting the threshold point as a “middle” boundary of the...

We consider in this paper that the reserve of an insurance company follows the classical model, in which the aggregate claim amount follows a compound Poisson process. Our goal is to minimize the ruin probability of the company assuming that the management can invest dynamically part of the...

This paper investigates a class of multiple-threshold models, called Multiple Threshold Double AR (MTDAR) models. A sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first-order MTDAR model. We study the Quasi-Maximum...

This paper studies the least squares estimator (LSE) of the multiple-regime threshold autoregressive (TAR) model and establishes its asymptotic theory. It is shown that the LSE is strongly consistent. When the autoregressive function is discontinuous over each threshold, the estimated thresholds...

Consider a compound Poisson process which is discretely observed with sampling interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\Delta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="normal">Δ</mi> </math> </EquationSource> </InlineEquation> until exactly <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> nonzero increments are obtained. The jump density and the intensity of the Poisson process are unknown. In this paper, we build and study parametric estimators...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this paper, we study the decision problem of a retailer, who wants to optimize the amount of shelf inventory of a particular product, given that the demand for the product is stochastic and replenishment lead times (from the store’s stockroom to the shelf) are negligible. The shelf...