Research output: Contribution to journal › Conference article › peer-review
Weconsider a PSI-process, that is a sequence of random variables (ζi), i = 0.1, ..., which is subordinated by a continuous-time non-decreasing integer-valued process N(t): φ(t) = ζN(t). Our main example is when N(t) itself is obtained as a subordination of the standard Poisson process Π(s) by a non-decreasing Lévy process S(t): N(t) = Π(S(t)).The values (ζi)one interprets as random claims, while their accumulated intensity S(t) is itself random. We show that in this case the process N(t) is a compound Poisson process of the stuttering type and its rate depends just on the value of theLaplace exponent of S(t) at 1. Under the assumption that the driven sequence (ζi) consists of i.i.d. random variables with finite variance we calculate a correlation function of the constructed PSI-process. Finally, we show that properly rescaled sums of such processes converge to the Ornstein-Uhlenbeck process in the Skorokhod space. We suppose that the results stated in the paper mightbe interesting for theorists and practitioners in insurance, in particular, for solution of reinsurance tasks.
Original language | English |
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Article number | 022107 |
Journal | Journal of Physics: Conference Series |
Volume | 2131 |
Issue number | 2 |
DOIs | |
State | Published - 29 Dec 2021 |
Event | Intelligent Information Technology and Mathematical Modeling 2021, IITMM 2021 - Divnomorskoe, Russian Federation Duration: 31 May 2021 → 6 Jun 2021 |
ID: 92425814