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- Publisher Website: 10.1007/s11425-022-2030-5
- Scopus: eid_2-s2.0-85168948052
- WOS: WOS:001064558600003
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Article: Asymptotics for joint tail probability of bidimensional randomly weighted sums with applications to insurance
| Title | Asymptotics for joint tail probability of bidimensional randomly weighted sums with applications to insurance |
|---|---|
| Authors | |
| Keywords | 62E20 62P05 91B05 asymptotic joint tail behavior dependence heavy-tailed distribution insurance risk model randomly weighted sum |
| Issue Date | 23-Aug-2023 |
| Publisher | Springer |
| Citation | Science China Mathematics, 2023, v. 67, p. 163-186 How to Cite? |
| Abstract | This paper studies the joint tail behavior of two randomly weighted sums ∑mi=1 ΘiXi and ∑nj=1θjYj for some m, n ∈ ℕ ∪{∞}, in which the primary random variables {Xi;i ∈ ℕ} and {Yi;i ∈ ℕ}, respectively, are real-valued, dependent and heavy-tailed, while the random weights {Θi, θi; i ∈ ℕ} are nonnegative and arbitrarily dependent, but the three sequences {Xi;i ∈ ℕ}, {Yi;i ∈ ℕ} and {Θi, θi;i ∈ ℕ} are mutually independent. Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights, we establish some (uniformly) asymptotic formulas for the joint tail probability of the two randomly weighted sums, expressing the insensitivity with respect to the underlying weak dependence structures. As applications, we consider both discrete-time and continuous-time insurance risk models, and obtain some asymptotic results for ruin probabilities. |
| Persistent Identifier | http://hdl.handle.net/10722/337948 |
| ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 1.060 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Yang, Y | - |
| dc.contributor.author | Chen, S | - |
| dc.contributor.author | Yuen, KC | - |
| dc.date.accessioned | 2024-03-11T10:25:08Z | - |
| dc.date.available | 2024-03-11T10:25:08Z | - |
| dc.date.issued | 2023-08-23 | - |
| dc.identifier.citation | Science China Mathematics, 2023, v. 67, p. 163-186 | - |
| dc.identifier.issn | 1674-7283 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/337948 | - |
| dc.description.abstract | <p>This paper studies the joint tail behavior of two randomly weighted sums ∑<sup><em>m</em></sup><sub><em>i</em>=1</sub> Θ<sub><em>i</em></sub><em>X</em><sub><em>i</em></sub> and ∑<sup><em>n</em></sup><sub><em>j</em>=1</sub><em>θ</em><sub><em>j</em></sub><em>Y</em><sub><em>j</em></sub> for some <em>m, n</em> ∈ ℕ ∪{∞}, in which the primary random variables {<em>X</em><sub><em>i</em></sub>;<em>i</em> ∈ ℕ} and {<em>Y</em><sub><em>i</em></sub>;<em>i</em> ∈ ℕ}, respectively, are real-valued, dependent and heavy-tailed, while the random weights {Θ<sub><em>i</em></sub>, θ<sub><em>i</em></sub>; <em>i</em> ∈ ℕ} are nonnegative and arbitrarily dependent, but the three sequences {<em>X</em><sub><em>i</em></sub>;<em>i</em> ∈ ℕ}, {<em>Y</em><sub><em>i</em></sub>;<em>i</em> ∈ ℕ} and {Θ<sub><em>i</em></sub>, θ<sub><em>i</em></sub>;<em>i</em> ∈ ℕ} are mutually independent. Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights, we establish some (uniformly) asymptotic formulas for the joint tail probability of the two randomly weighted sums, expressing the insensitivity with respect to the underlying weak dependence structures. As applications, we consider both discrete-time and continuous-time insurance risk models, and obtain some asymptotic results for ruin probabilities.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | Springer | - |
| dc.relation.ispartof | Science China Mathematics | - |
| dc.subject | 62E20 | - |
| dc.subject | 62P05 | - |
| dc.subject | 91B05 | - |
| dc.subject | asymptotic joint tail behavior | - |
| dc.subject | dependence | - |
| dc.subject | heavy-tailed distribution | - |
| dc.subject | insurance risk model | - |
| dc.subject | randomly weighted sum | - |
| dc.title | Asymptotics for joint tail probability of bidimensional randomly weighted sums with applications to insurance | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.1007/s11425-022-2030-5 | - |
| dc.identifier.scopus | eid_2-s2.0-85168948052 | - |
| dc.identifier.volume | 67 | - |
| dc.identifier.spage | 163 | - |
| dc.identifier.epage | 186 | - |
| dc.identifier.eissn | 1869-1862 | - |
| dc.identifier.isi | WOS:001064558600003 | - |
| dc.identifier.issnl | 1869-1862 | - |