The asymptotic ruin problem when the healthy and sick periods form an alternating renewal process
CM Ramsay - Insurance: Mathematics and Economics, 1984 - Elsevier
Abstract Let {T 1, Y 1}∞ i= 1 be a sequence of positive independent random variables. Let,
also, Z 1= βY′ 1− πT i, i= 1, 2,…, where Y′ 1= Max (0, Y i− w), w⩾ 0, and where β< 0 and
π is such that E (Z 1)< 0. We consider the random walk of partial sums S n= ϵ ni= 1 Z i in the
presence of an absorbing region (u,∞), u⩾ 0, and S 0≡ 0. Of interest is ψ (u)= Pr (S ̄≤ u)
where S̄= Sup (0, S 1, S 2,…, S n,…).
also, Z 1= βY′ 1− πT i, i= 1, 2,…, where Y′ 1= Max (0, Y i− w), w⩾ 0, and where β< 0 and
π is such that E (Z 1)< 0. We consider the random walk of partial sums S n= ϵ ni= 1 Z i in the
presence of an absorbing region (u,∞), u⩾ 0, and S 0≡ 0. Of interest is ψ (u)= Pr (S ̄≤ u)
where S̄= Sup (0, S 1, S 2,…, S n,…).
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