arXiv subjects

Fengyang Cheng

Publications and source records attributed to Fengyang Cheng.

4 recordsLinked to original sources

arXiv2017

A necessary and sufficient condition for the subexponentiality of product distribution

Let X and Y be two independent and nonnegative random variables with corresponding distributions F and G. Denote by H the distribution of the product XY , called the product convolution of F and G. Cline and Samorodnitsky (1994) proposed sufficient conditions for H to be subexponential, given the subexponentiality of F. Relying on a related result of Tang (2008) on the long-tail of product convolution, we obtain a necessary and sufficient condition for the subexponentiality of H, given that of F. We also study the reverse problem and obtain sufficient conditions for the subexponentiality of F given that of H. Finally, we apply the obtained results to the asymptotic study of the ruin probability in a discrete-time insurance risk model with stochastic returns.

math.PR↗

arXiv2017

The finite-time ruin probability of the nonhomogeneous Poisson risk model with conditionally independent subexponential claims

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common subexponential distribution. The paper also obtains some asymptotic relations of randomly weighted sums $\sum_{i=1}^n θ_iX_i$, in which the weights $θ_i$ $i=1,2,\cdots, n$ are positive random variables which are bounded above and the primary random variables $X_i$, $i=1,2,\cdots,n$ are conditionally independent and follow subexponential distributions.

math.PR↗

arXiv2016

The product of dependent random variables with applications to a discrete-time risk model

Let $X$ be a real valued random variable with an unbounded distribution $F$ and let $Y$ be a nonnegative valued random variable with a unbounded distribution $G$, which satisfy that \begin{eqnarray*} P(X>x|Y=y)\sim h(y)P(X>x) \end{eqnarray*} holds uniformly for $y\geq0$ as $x\to \infty$. Under the condition that $\overline{G}(bx)=o(\overline H(x))$ holds for all constant $b>0$, we proved that $F\in\mathcal{L}(γ)$ for some $γ\geq 0$ implied $H\in \mathcal{L}(γ/β_G)$ and that $F\in\mathcal{S}(γ)$ for some $γ\geq 0$ implied $H\in \mathcal{S}(γ/β_G)$, where $H$ is the distribution of the product $XY$, and $β_G$ is the right endpoint of $G$, that is, $β_G=\sup\{y:~G(y)<1\}\in (0,\infty],$ and when $β_G=\infty$, $γ/β_G$ is understood as 0. Furthermore, in a discrete-time risk model in which the net insurance loss and the stochastic discount factor are equipped with a dependence structure, a general asymptotic formula for the finite-time ruin probability is obtained when the net insurance loss has a subexponential tail.

math.PR↗

arXiv2016

Precise local large deviations for random sums with applications

In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common distribution $F$, where $F(x+Δ)=F((x, x+T])$ is an $\mathcal{O}$-regularly varying function for some fixed constant $T>0$(finite or infinite). We also obtain some results on precise local large deviation probabilities for the claim surplus process of generalized risk models in which the premium income until time $t$ is simply assumed to be a nondecreasing and nonnegative stochastic process. In particular, the results we obtained are also valid for the global case, i.e. case $T=\infty$.

math.PR↗