^{1,2}

^{3}

^{2}

^{1}

^{2}

^{3}

We propose a general continuous-time risk model with a constant interest rate. In this model, claims arrive according to an arbitrary counting process, while their sizes have dominantly varying tails and fulfill an extended negative dependence structure. We obtain an asymptotic formula for the finite-time ruin probability, which extends a corresponding result of Wang (2008).

In this paper, we consider the finite-time ruin probability with constant interest rate in a dependent general risk model. In this model, the claim sizes

If the claim sizes

Hereafter, all limit relationships hold for

In risk theory, heavy-tailed distributions are often used to model large claim amounts. They play a key role in insurance and finance. We will restrict the claim-size distribution

The asymptotic behavior of the ruin probability in the classical risk model has been extensively investigated in the literature. Klüppelberg and Stadtmüller [

In this paper, we are interested in the finite-time ruin probability. In this aspect, Tang [

In the independent general risk model introduced in Section

In the present paper, we aim to deal with the extended negatively dependent general risk model to get a similar result under

We call r.v.s

Motivated by the work of Wang [

In the dependent general risk model introduced in Section

The rest of the present paper consists of two sections. We give some lemmas and the proof of Theorem

In the sequel,

If a distribution

for any

it holds for every

By direct verification, END r.v.s have the following properties similar to those of ND r.v.s; see Lemma 3.1 of Liu [

(i) If r.v.s

(ii) If r.v.s

The following two lemmas play important roles in the proof of our main result.

Let

Following the proof of Lemma 2.3 of Tang [

Let, in the following,

In the dependent general risk model introduced in Section

We remark that if

We follow the line of the proof of Lemma 3.6 of Wang [

If

We use the idea in the proof of Theorem 2.2 of Wang [

To estimate the upper bound of

As for the lower bound of

If

In this section, we perform some numerical calculations to check the accuracy of the asymptotic relations obtained in Theorem

We assume that the claim sizes

Assume that the claim arrival process

Assign a value for the variable

Divide the close interval

For each

Generate the accident arrival time

Calculate the expression

Select the maximum value from

Repeat Step

Calculate the moment estimate of the finite-time ruin probability,

Repeat Step

For different value of

Comparison between the analog value and the theoretical result in Theorem

Theoretical result | Analog value | |
---|---|---|

0.5 | ||

1 | ||

2 | ||

5 |

The authors would like to thank the two referees for their useful comments on an earlier version of this paper. The revision of this work was finished during a research visit of the first author to Vilnius University. He would like to thank the Faculty of Mathematics and Informatics for its excellent hospitality. Research supported by National Natural Science Foundation of China (no. 11001052), China Postdoctoral Science Foundation (20100471365), National Science Foundation of Jiangsu Province of China (no. BK2010480), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 09KJD110003), Postdoctoral Research Program of Jiangsu Province of China (no. 0901029C), and Jiangsu Government Scholarship for Overseas Studies, Qing Lan Project.