The Sparre Andersen Risk Process with Investment and Debit Interest |
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Authors: | Zhao Yongxia |
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Institution: | School of Finance and Statistic, East China Normal University; School of Mathematical Sciences, Qufu Normal University |
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Abstract: | In this paper, we study absolute ruin
problems for the Sparre Andersen risk process with generalized
Erlang()-distributed inter-claim times, investment and debit
interest. We first give a system of integro-differential equations
with certain boundary conditions satisfied by the expected
discounted penalty function at absolute ruin. Second, we obtain a
defective renewal equation under some special cases, then based on
the defective renewal equation we derive two asymptotic results for
the expected discounted penalty function when the initial surplus
tends to infinity for the light-tailed claims and heavy-tailed
claims, respectively. Finally, we investigate some explicit
solutions and numerical results for generalized Erlang(2)
inter-claim times and exponential claims. |
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Keywords: | |
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