Stochastic Discounting, Aggregate Claims, and the Bootstrap
Obtaining good estimates for the distribution function of random variables like S=∑i=1 ∞Z1⋯ ZiYi('perpetuity') and SN(t)=∑i=1 N(t)Yi('aggregate claim amount'), where the (Yi), (Zi) are independent i.i.d. sequences and (N(t)) is a general point process,...
Veröffentlicht in: | Advances in Applied Probability. - Applied Probability Trust. - 26(1994), 1, Seite 183-206 |
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1. Verfasser: | |
Weitere Verfasser: | , |
Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
1994
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Zugriff auf das übergeordnete Werk: | Advances in Applied Probability |
Schlagworte: | Bootstrap Perpetuity Probability metrics Risk theory Stochastic discounting Mathematics Economics |
Zusammenfassung: | Obtaining good estimates for the distribution function of random variables like S=∑i=1 ∞Z1⋯ ZiYi('perpetuity') and SN(t)=∑i=1 N(t)Yi('aggregate claim amount'), where the (Yi), (Zi) are independent i.i.d. sequences and (N(t)) is a general point process, is a key question in insurance mathematics. In this paper, we show how suitably chosen metrics provide a theoretical justification for bootstrap estimation in these cases. In the perpetuity case, we also give a detailed discussion of how the method works in practice. |
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ISSN: | 00018678 |
DOI: | 10.2307/1427586 |