Risk Theory

Arjun K. Gupta (), Wei-Bin Zeng () and Yanhong Wu ()
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Arjun K. Gupta: Bowling Green State University, Department of Mathematics and Statistics
Wei-Bin Zeng: University of Louisville, Department of Mathematics
Yanhong Wu: California State University Stanislaus, Department of Mathematics

Chapter Chapter 9 in Probability and Statistical Models, 2010, pp 179-198 from Springer

Abstract: Abstract Suppose the claims arrive according to a Poisson process {N(t)} with rate λ and interarrival intervals {X 1, ⋯, X n , ⋯ }. The consecutive claim amounts {Y 1, ⋯, Y n , ⋯ } are identically and independently distributed with continuous distribution F(y) with mean μ > 0, and independent of the arrival times. The premier rate c satisfies c ∕ λ > μ, and $$c = \lambda \mu (1 + \theta )$$ . This guarantees the profitability in the long run. The risk process R t is defined as $${R}_{t} = ct -{\sum }_{i=1}^{N(t)}{Y }_{ i}.$$ For initial capital reserve U 0 = u, we define the surplus process as $$U_t = u + R_t$$ and the time of ruin as $$T = \inf \{t > 0: U_t = u + R_t

Keywords: Moment Generate Function; Risk Process; Claim Size; Claim Amount; Renewal Equation (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-8176-4987-6_9

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