Risk Theory

  • Arjun K. Gupta
  • Wei-Bin Zeng
  • Yanhong Wu


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
$$T = \inf \{t > 0: U_t = u + R_t < 0\}.$$


Moment Generate Function Risk Process Claim Size Claim Amount Renewal Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  3. 3.Department of MathematicsCalifornia State University StanislausTurlockUSA

Personalised recommendations