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2 results

  • Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models

  • Part of
  • Shijie Wang, Wensheng Wang
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 4 / December 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 889-900
    Print publication:
    December 2007
    • Article
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  • Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij, j ≥ 1}, i = 1,…,k. In this paper we investigate large deviations for both partial sums S(k; n1,…,nk) = ∑i=1k ∑j=1niXij and random sums S(k; t) = ∑i=1k ∑j=1Ni (t)Xij, where Ni(t), i = 1,…,k, are counting processes for the claim number. The obtained results extend some related classical results.

  • Negative binomial sums of random variables and discounted reward processes

  • Part of
  • William L. Cooper
  • Journal:
    Journal of Applied Probability / Volume 35 / Issue 3 / September 1998
    Published online by Cambridge University Press:
    14 July 2016, pp. 589-599
    Print publication:
    September 1998

  • Given a sequence of random variables (rewards), the Haviv–Puterman differential equation relates the expected infinite-horizon λ-discounted reward and the expected total reward up to a random time that is determined by an independent negative binomial random variable with parameters 2 and λ. This paper provides an interpretation of this proven, but previously unexplained, result. Furthermore, the interpretation is formalized into a new proof, which then yields new results for the general case where the rewards are accumulated up to a time determined by an independent negative binomial random variable with parameters k and λ.