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Notes: Sumario: The paper examines the conditional expectation of one component of a sum, a quantity that plays a central role in actuarial applications such as risk-sharing rules and capital allocation. While the monotonicity of this function is usually linked to log-concave densities, that assumption excludes heavy-tailed distributions. The study investigates cases where regularly varying tails cause this conditional expectation to lose its monotonic behavior and describes its asymptotic properties when the total sum becomes large. The analysis is further extended to zero-inflated distributions, sums involving more than two random variables, and dependence structures modeled through Farlie-Gumbel-Morgenstern copulas. The paper concludes with implications for risk sharing and capital allocation, supported by numerous numerical examples.Related records: En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 12/05/2025 Volume 55 Issue 2 - may 2025 , p. 449 - 485Materia / lugar / evento: Matemática del seguro Cálculo actuarial Estadística matemática Gestión de riesgos Distribuciones estadísticas Condicionados Capital allocation Distribución de riesgos Otros autores: Ortega Jiménez, Patricia
Christian-Yann, Robert
International Actuarial Association
Other categories: 6

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Conditional expectations given the sum of independent random variables with regularly varying densities