On occupation times for a risk process with reserve-dependent premium

Sung Nok CHIU*, Chuancun Yin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a < b, we study the occupation time Ta,b(t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of Ta,b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.

Original languageEnglish
Pages (from-to)245-255
Number of pages11
JournalStochastic Models
Volume18
Issue number2
DOIs
Publication statusPublished - 2002

Scopus Subject Areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

User-Defined Keywords

  • Duration of negative surplus
  • Occupation time
  • Piecewise deterministic Markov process
  • Risk theory
  • Ruin

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