The asymptotic ruin problem when the healthy and sick periods form an alternating renewal process |
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Authors: | Colin M Ramsay |
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Institution: | Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada |
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Abstract: | Let {T1, Y1}∞i=1 be a sequence of positive independent random variables. Let, also, Z1 = βY′1 ? πTi, i = 1, 2, …, where Y′1 = Max(0, Yi ? w), w ? 0, and where β < 0 and π is such that E(Z1) < 0. We consider the random walk of partial sums Sn = ?ni=1Zi in the presence of an absorbing region (u, ∞), u ? 0, and S0 ≡ 0. Of interest is where S? = Sup(0, S1, S2, …, Sn, …). |
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Keywords: | Alternating renewal process P-solution Random walk of partial sums Ruin |
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