Tail asymptotic of discounted aggregate claims with compound dependence under risky investment

ABSTRACT

This paper considers the tail asymptotic of discounted aggregate claims with compound dependence under risky investment. The price of risky investment is modeled by a geometric Lévy process, while claims are modeled by a one-sided linear process whose innovations further obeying a so-called upper tail asymptotic independence. When the innovations are heavy tailed, we derive some uniform asymptotic formulas. The results show that the linear dependence has significant impact on the tail asymptotic of discounted aggregate claims but the upper tail asymptotic independence is negligible.

KEYWORDS:

• Asymptotic independence
• Heavy tail
• Investment returns
• Lévy process
• One-sided linear process.

MATHEMATICS SUBJECT CLASSICATION:

• 62E20
• 62P05

Additional information

Funding

Guo’s work is supported by the National Natural Science Foundation of China (Grant No. 71501100) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Wang’s work is supported by the National Natural Science Foundation of China (Grant No. 71271042). Peng’s work is supported by the National Natural Science Foundation of China (Grant No. 71501025).