arXiv subjects

Zhanyi Jiao

Publications and source records attributed to Zhanyi Jiao.

5 recordsLinked to original sources

arXiv2026

Comparative e-backtests for general risk measures

Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the performance of an internal model relative to benchmark models. We develop a non-parametric sequential framework for comparative backtests of general elicitable risk measures using e-values and e-processes. The proposed methods provide anytime-valid inference and remain robust under dependence and model misspecification. In particular, we propose a modified three-zone approach based on weak dominance, which yields more informative conclusions in comparative backtesting. As a technical building block, we also construct general standard e-backtests for identifiable risk measures and characterize the associated e-values and e-processes. The resulting procedures apply to a broad class of commonly used risk measures, including the mean, variance, Value-at-Risk, Expected Shortfall, and expectiles. Simulation studies and empirical analyses illustrate the effectiveness of the proposed approach.

stat.ME↗

arXiv2024

Worst-case values of target semi-variances with applications to robust portfolio selection

The expected regret and target semi-variance are two of the most important risk measures for downside risk. When the distribution of a loss is uncertain, and only partial information of the loss is known, their worst-case values play important roles in robust risk management for finance, insurance, and many other fields. Jagannathan (1977) derived the worst-case expected regrets when only the mean and variance of a loss are known and the loss is arbitrary, symmetric, or non-negative. While Chen et al. (2011) obtained the worst-case target semi-variances under similar conditions but focusing on arbitrary losses. In this paper, we first complement the study of Chen et al. (2011) on the worst-case target semi-variances and derive the closed-form expressions for the worst-case target semi-variance when only the mean and variance of a loss are known and the loss is symmetric or non-negative. Then, we investigate worst-case target semi-variances over uncertainty sets that represent undesirable scenarios faced by an investors. Our methods for deriving these worst-case values are different from those used in Jagannathan (1977) and Chen et al. (2011). As applications of the results derived in this paper, we propose robust portfolio selection methods that minimize the worst-case target semi-variance of a portfolio loss over different uncertainty sets. To explore the insights of our robust portfolio selection methods, we conduct numerical experiments with real financial data and compare our portfolio selection methods with several existing portfolio selection models related to the models proposed in this paper.

q-fin.RM↗

arXiv2024

Testing mean and variance by e-processes

We address the problem of testing conditional mean and conditional variance for non-stationary data. We build e-values and p-values for four types of non-parametric composite hypotheses with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality, and their combination. Using the obtained e-values and p-values, we construct tests via e-processes, also known as testing by betting, as well as some tests based on combining p-values for comparison. Although we mainly focus on one-sided tests, the two-sided test for the mean is also studied. Simulation and empirical studies are conducted under a few settings, and they illustrate features of the methods based on e-processes.

math.ST↗

arXiv2023

A reverse ES (CVaR) optimization formula

The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of a linear real function plus a scaled mean excess function. We establish a reverse ES optimization formula, which says that a mean excess function at any fixed threshold is the maximum of an ES curve minus a linear function. Despite being a simple result, this formula reveals elegant symmetries between the mean excess function and the ES curve, as well as their optimizers. The reverse ES optimization formula is closely related to the Fenchel-Legendre transforms, and our formulas are generalized from ES to optimized certainty equivalents, a popular class of convex risk measures. We analyze worst-case values of the mean excess function under two popular settings of model uncertainty to illustrate the usefulness of the reverse ES optimization formula, and this is further demonstrated with an application using insurance datasets.

q-fin.RM↗

arXiv2023

An axiomatic theory for anonymized risk sharing

We study an axiomatic framework for anonymized risk sharing. In contrast to traditional risk sharing settings, our framework requires no information on preferences, identities, private operations and realized losses from the individual agents, and thereby it is useful for modeling risk sharing in decentralized systems. Four axioms natural in such a framework -- actuarial fairness, risk fairness, risk anonymity, and operational anonymity -- are put forward and discussed. We establish the remarkable fact that the four axioms characterizes the conditional mean risk sharing rule, revealing the unique and prominent role of this popular risk sharing rule among all others in relevant applications of anonymized risk sharing. Several other properties and their relations to the four axioms are studied, as well as their implications in rationalizing the design of some sharing mechanisms in practice.

econ.TH↗