Abstract
The asymptotic behavior of the recovery probability for the dual renewal risk model with constant interest and debit force is studied. By means the idea of Markov Skeleton method, we studied the times that the random premium incomes happened and transformed the continuous time model into a discrete time model. By investigating the fluctuations of this discrete time model, we obtained the asymptotic behavior when the random premium income belongs to a kind of heavy-tailed distributions.
Highlights
The classical risk model is specified asU (t) = x + ct − S (t), (1)where x ≥ 0 is the initial surplus and c is the constant rate at which the premiums are received
More details about the surplus process can be found in Asmussen and Albrecher [1] and Rolski et al [2]
There is a constant consumption in the dual risk model; it has occasionally happened that the surplus of dual risk model is negative; in this case, the decision maker will care the probability that the surplus of the model became positive; we define this probability as the “recovery probability.”
Summary
Where x ≥ 0 is the initial surplus and c is the constant rate at which the premiums are received. There is a constant consumption in the dual risk model; it has occasionally happened that the surplus of dual risk model is negative; in this case, the decision maker will care the probability that the surplus of the model became positive; we define this probability as the “recovery probability.”. This conception is of both theoretical value and practical relevance.
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