Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims

Yang, Haizhong; Li, Jinzhu

doi:10.1016/j.insmatheco.2014.07.007

Cited by 39 publications

(9 citation statements)

References 11 publications

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“…[5] considered an independent renewal model with no interest force and consistently varying tailed claims. Later, [22], [14] and [25] studied a dependent (delayed) renewal risk model with nonnegative constant interest force, in which the claim vectors (X…”

Section: Yang Yang Kaiyong Wang Jiajun Liu and Zhimin Zhangmentioning

confidence: 99%

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Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Yang¹,

Wang²,

Liu³

et al. 2019

Journal of Industrial &Amp; Management Optimization

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Consider a bidimensional risk model with two geometric Lévy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Lévy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.

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Section: Yang Yang Kaiyong Wang Jiajun Liu and Zhimin Zhangmentioning

confidence: 99%

“…, by letting to be sufficiently small. For another side, as done in (22) and (24), we have that for all 0…”

Section: Proposition 2 Consider the Risk Modelmentioning

confidence: 99%

Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Yang¹,

Wang²,

Liu³

et al. 2019

Journal of Industrial &Amp; Management Optimization

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“…In Li (2017), he considered a renewal risk model with constant force of interest and Brownian perturbation, and derived for the finite-time ruin probability a precise asymptotic expansion. In Yang and Li (2014), they studied a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Some asymptotic results of the ruin probabilities in a bidimensional renewal risk model with Brownian perturbation

Song

2019

Filomat

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In this paper, a bidimensional renewal risk model with constant force of interest and Brownian perturbation is considered. Assuming that the claim-size distribution function is from the subexponential class, three types of the finite-time ruin probabilities under this model are discussed. We obtain the asymptotic formulas for the three types, which hold uniformly for any finite-time horizon. where x 1 , x 2 ≥ 0 denote the initial surplus, r ≥ 0 the force of interest, p 1 , p 2 ≥ 0 the premium rate, δ 1 , δ 2 ≥ 0 the volatility factor, {B 1 (t), B 2 (t); t ≥ 0} the diffusion perturbation which are independent standard Brownian motions, {X 1j , j ≥ 1; X 2i , i ≥ 1} the sequence of claim sizes which are independent and identically distributed(i.i.d), {Y 1k , k ≥ 1; Y 2i , i ≥ 1} the sequence of claim sizes which are independent and identically distributed(i.i.d). We denote by τ (i) k , k = 1, 2, ..., the arrival times of the renewal counting process N i (t), i = 1, 2, 3. And N 1 (t), N 2 (t), N 3 (t) are three independent renewal processes. In reality, the common shock N 3 (t) can depict the effect of a natural disaster that causes various kinds of insurance claims. Throughout this paper, we assume that {X 1 j , j ≥ 1; X 2i , i ≥ 1}, {Y 1k , k ≥ 1; Y 2i , i ≥ 1}, {B 1 (t); t ≥ 0}, {B 2 (t); t ≥ 0} and {N i (t); t ≥ 0, i = 1, 2, 3} are mutually independent. Define the ruin times of the two marginal processes as: T(x i) = inf {t : U i (t) < 0|U i (0) = x i } , i = 1, 2.

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“…Hence, the risk theory for multidimensional risk models is of great interest, particularly the analysis of multidimensional risk models. However, most works on this topic focus on typical risk models with assumed independence among claim sizes from different businesses subject to mathematical tractability; see Li et al [13], Chen et al [3], Zhang and Wang [21], Chen et al [4], Hu and Jiang [8], Yang and Li [20], and Li [11], among others.…”

Section: Introductionmentioning

confidence: 99%

Approximation of the Tail Probabilities for Bidimensional Randomly Weighted Sums With Dependent Components

Shen

2018

Prob. Eng. Inf. Sci.

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Let $\left\{ {{\bi X}_k = {(X_{1,k},X_{2,k})}^{\top}, k \ge 1} \right\}$ be a sequence of independent and identically distributed random vectors whose components are allowed to be generally dependent with marginal distributions being from the class of extended regular variation, and let $\left\{ {{\brTheta} _k = {(\Theta _{1,k},\Theta _{2,k})}^{\top}, k \ge 1} \right\}$ be a sequence of nonnegative random vectors that is independent of $\left\{ {{\bi X}_k, k \ge 1} \right\}$. Under several mild assumptions, some simple asymptotic formulae of the tail probabilities for the bidimensional randomly weighted sums $\left( {\sum\nolimits_{k = 1}^n {\Theta _{1,k}} X_{1,k},\sum\nolimits_{k = 1}^n {\Theta _{2,k}} X_{2,k}} \right)^{\rm \top }$ and their maxima $({{\max} _{1 \le i \le n}}\sum\nolimits_{k = 1}^i {\Theta _{1,k}} X_{1,k},{{\max} _{1 \le i \le n}}\sum\nolimits_{k = 1}^i {\Theta _{2,k}} X_{2,k})^{\rm \top }$ are established. Moreover, uniformity of the estimate can be achieved under some technical moment conditions on $\left\{ {{\brTheta} _k, k \ge 1} \right\}$. Direct applications of the results to risk analysis are proposed, with two types of ruin probability for a discrete-time bidimensional risk model being evaluated.

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Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims

Cited by 39 publications

References 11 publications

Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Some asymptotic results of the ruin probabilities in a bidimensional renewal risk model with Brownian perturbation

Approximation of the Tail Probabilities for Bidimensional Randomly Weighted Sums With Dependent Components

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