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- W4255781603 abstract "We consider the operation of an insurer with a large initial surplus x >0. The insurer's surplus process S ( t ) (with S(0)= x ) evolves in the range S(t)≥ 0 as a generalized renewal process with positive mean drift and with jumps at time epochs T 1 , T 2 ,…. At the time T η( x ) when the process S ( t ) first becomes negative, the insurer's ruin (in the ‘classical’ sense) occurs, but the insurer can borrow money via a line of credit. After this moment the process S ( t ) behaves as a solution to a certain stochastic differential equation which, in general, depends on the indebtedness, - S ( t ). This behavior of S ( t ) lasts until the time θ( x , y ) at which the indebtedness reaches some ‘critical’ level y >0. At this moment the line of credit will be closed and the insurer's absolute ruin occurs with deficit - S (θ( x , y )). We find the asymptotics of the absolute ruin probability and the limiting distributions of η( x ), θ( x , y ), and - S (θ( x , y )) as x → ∞, assuming that the claim distribution is regularly varying. The second-order approximation to the absolute ruin probability is also obtained. The abovementioned results are obtained by using limiting theorems for the joint distribution of η( x ) and - S ( T η( x ) )." @default.
- W4255781603 created "2022-05-12" @default.
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- W4255781603 date "2009-12-01" @default.
- W4255781603 modified "2023-10-14" @default.
- W4255781603 title "Insurance with borrowing: first- and second-order approximations" @default.
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- W4255781603 doi "https://doi.org/10.1017/s0001867800003785" @default.
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