arXiv subjects

Taizhong Hu

Publications and source records attributed to Taizhong Hu.

9 recordsLinked to original sources

arXiv2026

Stochastic dominance for linear combinations of infinite-mean risks

In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that includes many commonly used heavy-tailed distributions and show that within this class, a linear combination of random variables is stochastically larger when its weight vector is smaller in the sense of majorization order. We proceed to study the case where each random variable is a compound Poisson sum and demonstrate that if the stochastic dominance relation holds, the summand of the compound Poisson sum belongs to our new class of distributions. Additional discussions are presented for stable distributions.

math.PR↗

arXiv2026

Distributionally Robust Reinsurance under Robust Optimized Certainty Equivalent Risk Measure

In this paper, we introduce a class of preference robust risk measures-\emph{robust optimized certainty equivalents} (ROCE)-which encompasses several widely used measures, including Conditional Value-at-Risk and expectiles, as special cases. Motivated by recent developments in distributionally robust optimal reinsurance (DROR), we investigate DROR problems under the ROCE risk measure and consider two prominent uncertainty sets: the mean-variance uncertainty set and the Wasserstein uncertainty set. For the mean-variance uncertainty set, we reformulate the infinite-dimensional optimization problem into a finite-dimensional one by showing that it suffices to consider three-point distributions. This leads to a unified and explicit formulation for a broad class of ROCE risk measures and offers a simplified framework that also recovers earlier results for Conditional Value-at-Risk and expectiles. For the Wasserstein uncertainty set, we also derive a tractable finite-dimensional formulation. The resulting data-driven models enable efficient computation and facilitate a systematic comparison between moment-based and Wasserstein-based uncertainty sets in the optimal deductible design. Numerical experiments are exhibited to illustrate the performance of our reformulated programs.

math.OC↗

arXiv2026

Further Developments on Stochastic Dominance for Convex Combinations of Infinite-Mean Random Variables

In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random variables that encompass many common heavy-tailed distributions. A key result demonstrates that the weighted sum of iid random variables from these classes is stochastically larger than any individual random variable in the sense of the first-order stochastic dominance. This paper systematically investigates the properties and inclusion relationships among these distribution classes, and extends some existing results to more practical scenarios. Furthermore, we analyze the case where each random variable follows a compound binomial distribution, establishing necessary and sufficient conditions for the preservation of the aforementioned stochastic dominance relation.

math.PR↗

arXiv2026

Moment inequalities for higher-order (inverse) stochastic dominance

Stochastic dominance has been studied extensively, particularly in the finance and economics literature. In this paper, we obtain two results. First, necessary conditions for higher-order inverse stochastic dominance are developed. These conditions, which involve moment inequalities of the minimum order statistics, are analogous to the ones obtained by Fishburn (1980b) for usual higher-order stochastic dominance. Second, we investigate how background risk variables influence usual higher-order stochastic dominance. The main result generalizes the ones in Pomatto et al. (2020) from the first-order and second-order stochastic dominance to the higher-order.

math.PR↗

arXiv2025

Negative Dependence in Knockout Tournaments

Negative dependence in tournaments has received attention in the literature. The property of negative orthant dependence (NOD) was proved for different tournament models with a special proof for each model. For general round-robin tournaments and knockout tournaments with random draws, Malinovsky and Rinott (2023) unified and simplified many existing results in the literature by proving a stronger property, negative association (NA). For a knockout tournament with a non-random draw, Malinovsky and Rinott (2023) presented an example to illustrate that S is NOD but not NA. However, their proof is not correct. In this paper, we establish the properties of negative regression dependence (NRD), negative left-tail dependence (NLTD) and negative right-tail dependence (NRTD) for a knockout tournament with a random draw and with players being of equal strength. For a knockout tournament with a non-random draw and with equal strength, we prove that S is NA and NRTD, while S is, in general, not NRD or NLTD.

math.PR↗

arXiv2025

Norms Based on Generalized Expected-Shortfalls and Applications

This paper proposes a novel class of generalized Expected-Shortfall (ES) norms constructed via distortion risk measures, establishing a unified analytical framework for risk quantification. The proposed norms extend conventional ES methodology by incorporating flexible distortion functions. Specifically, we develop the mathematical duality theory for generalized-ES norms to support portfolio optimization tasks, while demonstrating their practical utility through projection problem solutions. The generalizedES norms are also applied to detect anomalies of financial time series data.

q-fin.RM↗

arXiv2025

Extreme-case Range Value-at-Risk under Increasing Failure Rate

The extreme cases of risk measures, when considered within the context of distributional ambiguity, provide significant guidance for practitioners specializing in risk management of quantitative finance and insurance. In contrast to the findings of preceding studies, we focus on the study of extreme-case risk measure under distributional ambiguity with the property of increasing failure rate (IFR). The extreme-case range Value-at-Risk under distributional uncertainty, consisting of given mean and/or variance of distributions with IFR, is provided. The specific characteristics of extreme-case distributions under these constraints have been characterized, a crucial step for numerical simulations. We then apply our main results to stop-loss and limited loss random variables under distributional uncertainty with IFR.

q-fin.RM↗

arXiv2025

Diversification for infinite-mean Pareto models without risk aversion

We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified portfolio of iid extremely heavy-tailed Pareto random variables is larger in the sense of first-order stochastic dominance. This result is further generalized for Pareto random variables caused by triggering events, random variables with tails being Pareto, bounded Pareto random variables, and positively dependent Pareto random variables. These results provide an important implication in investment: Diversification of extremely heavy-tailed Pareto profits uniformly increases investors' profitability, leading to a diversification benefit. Remarkably, different from the finite-mean setting, such a diversification benefit does not depend on the decision maker's risk aversion.

q-fin.PM↗

arXiv2013

Some inequalities of linear combinations of independent random variables: II

Linear combinations of independent random variables have been extensively studied in the literature. However, most of the work is based on some specific distribution assumptions. In this paper, a companion of (J. Appl. Probab. 48 (2011) 1179-1188), we unify the study of linear combinations of independent nonnegative random variables under the general setup by using some monotone transforms. The results are further generalized to the case of independent but not necessarily identically distributed nonnegative random variables. The main results complement and generalize the results in the literature including (In Studies in Econometrics, Time Series, and Multivariate Statistics (1983) 465-489 Academic Press; Sankhyā Ser. A 60 (1998) 171-175; Sankhyā Ser. A 63 (2001) 128-132; J. Statist. Plann. Inference 92 (2001) 1-5; Bernoulli 17 (2011) 1044-1053).

math.ST↗