arXiv subjects

José M. Zapata

Publications and source records attributed to José M. Zapata.

5 recordsLinked to original sources

arXiv2026

Logarithmic Large Deviations for Heavy-Tailed Randomly Stopped Sums

We derive logarithmic large-deviation asymptotics for randomly stopped sums with nonnegative summands satisfy a weak form of regular variation. Our approach is based on a count-scale condition that controls the logarithmic order of the random number of summands and does not require relative concentration around its expectation. A main advantage of the framework is that it applies to every renewal count, without moment, regular-variation, or domain-of-attraction assumptions on the interarrival distribution. In particular, it covers infinite-mean interarrival regimes in which relative concentration may fail. It is proven that the mean renewal count is an admissible count scale even when relative concentration fails. We further apply the results to finite heterogeneous insurance portfolios, obtaining dependence-robust asymptotics for unions and weighted aggregate losses, as well as explicit joint shortfall costs under block independence.

math.PR↗

arXiv2026

Sharp large deviation estimates for heavy-tailed extrema

We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for exceedance probabilities at thresholds that grow faster than the natural extreme-value scaling. As an application, we derive the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim.

math.PR↗

arXiv2025

Sharp large deviation estimates for Gaussian extrema

We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d.\ standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than the classical Gumbel limit.

math.PR↗

arXiv2025

Stochastic dominance of sums of risks under dependence conditions

We provide conditions for the stochastic dominance comparisons of a risk $X$ and an associated risk $X+Z$, where $Z$ represents the uncertainty due to the environment and where $X$ and $Z$ can be dependent. The comparisons depend on both the copula $C$ between the distributions of $X$ and $Z$ and on the distribution of $Z$. We provide two different conditions for $C$ which represents new positive dependence properties. Regarding $Z$, we need some symmetry or asymmetry (skew) properties. Some illustrative examples are provided.

math.ST↗

arXiv2025

On independence and large deviations for sublinear expectations

We prove by counterexample that a large deviation principle established by Chen and Feng [{\em Comm. Statist. Theory Methods} {\bf 45} (2016), 400--412] in the framework of sublinear expectations is incorrect. That implies that the rate function cannot, in general, be obtained by computing the Fenchel transform of the cumulant generating function, as is the case for ordinary probabilities. We derive a corrected version of that result and show that the original presentation holds under a stronger independence assumption.

math.PR↗