Web renewal counting processes and their applications in insurance

Abstract

Abstract This paper investigates a nonstandard renewal counting process with dependent inter-arrival times-web renewal process. Several limit properties, including the tail of the exponential moment which is a crucial condition in many situations, are obtained. Then the results are applied in insurance to derive precise large deviations and moderate deviation formulas for the aggregate amount of claims.

Keywords

• Renewal processes
• Dependence
• Web Markov skeleton processes
• Precise large deviations
• Moderate deviations