Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate

This paper gives an asymptotically equivalent formula for the finite-time ruin probability of a nonstandard risk model with a constant interest rate, in which both claim sizes and inter-arrival times follow a certain dependence structure. This new dependence structure allows the underlying random variables to be either positively or negatively dependent. The obtained asymptotics hold uniformly in a finite time interval. Especially, in the renewal risk model the uniform asymptotics of the finite-time ruin probability for all times have been given. The obtained results have extended and improved some corresponding results.  

跳扩散市场投资组合研究

研究了连续时间动态均值-方差投资组合选择问题.假设风险资产价格服从跳跃-扩散过程且具有卖空约束.投资者的目标是在给定期望终止时刻财富条件下,最小化终止时刻财富的方差.通过求解模型相应的Hamilton-Jacobi-Bellmen方程,得到了最优投资策略及有效前沿的显示解.结果显示,风险资产的卖空约束及价格过程的跳跃因素对最优投资策略及有效前沿的是不可忽略的.  

Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest

In the paper, we study three types of finite-time ruin probabilities in a diffusion-perturbed bidimensional risk model with constant force of interest, pairwise strongly quasi-asymptotically independent claims and two general claim arrival processes, and obtain uniformly asymptotic formulas for times in a finite interval when the claims are both long-tailed and dominatedly-varying-tailed. In particular, with a certain dependence structure among the inter-arrival times, these formulas hold uniformly for all times when the claims are pairwise quasi-asymptotically independent and consistently-varying-tailed.  

On closure properties of heavy-tailed distributions for random sums*

We investigate some closure properties of heavy-tailed distributions for random sums. We first consider the random sums with independent or some certain dependent long-tailed increments. We also consider the real-valued increments with dominatedly varying-tailed distributions under extended negative dependence and obtain two results on necessary and sufficient conditions or sufficient conditions for the closure on random sums.  

Power Variation of Subfractional Brownian Motion and Application

In this paper, we consider the power variation of subfractional Brownian motion. As an application, we introduce a class of estimators for the index of a subfractional Brownian motion and show that they are strongly consistent.  

On asymptotic equivalence among the solutions of some defective renewal equations

We obtain some sufficient conditions for mutually asymptotic equivalence among solutions of some defective renewal equations, where the related distributions can be heavy-tailed but are not required to be subexponential. Particularly, the paper make clearer the asymptotically equivalent relations between the ruin probability and the function introduced by Gerber et al. [H.U. Gerber, M.J. Goovaerts, and R. Kaas, On the probability and severity of ruin, Astin Bull., 17:151–163, 1987] for the standard renewal risk model. The results we obtain modify, improve, and extend some existing results.  

Information granulation and uncertainty measures in interval-valued intuitionistic fuzzy information systems

Information granulation and entropy are main approaches for investigating the uncertainty of information systems, which have been widely employed in many practical domains. In this paper, information granulation and uncertainty measures for interval-valued intuitionistic fuzzy binary granular structures are addressed. First, we propose the representation of interval-valued intuitionistic fuzzy information granules and examine some operations of interval-valued intuitionistic fuzzy granular structures. Second, the interval-valued intuitionistic fuzzy information granularity is introduced to depict the distinguishment ability of an interval-valued intuitionistic fuzzy granular structure (IIFGS), which is a natural extension of fuzzy information granularity. Third, we discuss how to scale the uncertainty of an IIFGS using the extended information entropy and the uncertainty among interval-valued intuitionistic fuzzy granular structures using the expanded mutual information derived from the presented intuitionistic fuzzy information entropy. Fourth, we discovery the relationship between the developed interval-valued intuitionistic fuzzy information entropy and the intuitionistic fuzzy information granularity presented in this paper.  

A note on a dependent risk model with constant interest rate

For a dependent risk model with constant interest rate, in which the claim sizes form a sequence of upper tail asymptotically independent and identically distributed random variables, and their inter-arrival times are another sequence of widely lower orthant dependent and identically distributed random variables, we will give an asymptotically equivalent formula for the finite-time ruin probability. The obtained asymptotics holds uniformly in an arbitrarily finite-time interval.  

On a jump-type stochastic fractional partial differential equation with fractional noises

We study a class of stochastic fractional partial differential equations of order α>1$\alpha >1$ driven by a (pure jump) Lévy space–time white noise and a fractional noise. We prove the existence and uniqueness of the global mild solution by the fixed point principle under some suitable assumptions.  

Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables

In this paper the authors study the convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. The results extend and improve the corresponding theorems of T.C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance, Int. J. Math. Math. Sci 20 (1997), 375–382.