arXiv subjects

Chengxin Yan

Publications and source records attributed to Chengxin Yan.

5 recordsLinked to original sources

arXiv2026

Glivenko--Cantelli Theorems for Integrated Volatility Functionals in Pure-Jump Semimartingales with an Application to Cryptocurrency Markets

We develop a two-step procedure for estimating integrated volatility functionals, defined through the occupation measure of the latent spot volatility process, when the asset price is a pure-jump semimartingale. In the first step, block-based estimators formed from absolute powers of high-frequency increments uniformly approximate local averages of powers of volatility. In the second step, these estimates are aggregated into an empirical occupation measure. Since price increments have infinite variance in this setting, arguments based on local Gaussianity are unavailable, and the uniform theory instead rests on maximal inequalities tailored to the stable regime. We establish Glivenko--Cantelli-type uniform consistency over classes of bounded monotone, Lipschitz-in-parameter, and locally H\"older test functions. These results deliver consistent estimation of volatility occupation times and quantiles, together with an argmax-consistency theory for $M$-estimators built on nonparametrically recovered latent processes. We further propose a stability-based rule for selecting the power index of the volatility estimator, which tracks an infeasible ex ante optimal choice closely in Monte Carlo experiments. An application to high-frequency cryptocurrency markets illustrates the framework in a jump-dominated, heavy-tailed environment.

math.ST↗

arXiv2026

Nonparametric inference for spot volatility in pure-jump semimartingales

We provide a comprehensive analysis of spot volatility inference in pure-jump semimartingales under two asymptotic settings: fixed-$k$, where each local window uses a fixed number of observations, and large-$k$, where this number grows with sampling frequency. For both active- and possibly inactive-jump settings, we derive generally nonstandard, typically non-Gaussian limit distributions and establish valid inference, including when the jump-activity index is consistently estimated. Simulations show that fixed-$k$ asymptotics offer markedly better finite-sample accuracy, underscoring their practical advantage for nonparametric spot volatility inference.

math.ST↗

arXiv2025

WGSR-Bench: Wargame-based Game-theoretic Strategic Reasoning Benchmark for Large Language Models

Recent breakthroughs in Large Language Models (LLMs) have led to a qualitative leap in artificial intelligence' s performance on reasoning tasks, particularly demonstrating remarkable capabilities in mathematical, symbolic, and commonsense reasoning. However, as a critical component of advanced human cognition, strategic reasoning, i.e., the ability to assess multi-agent behaviors in dynamic environments, formulate action plans, and adapt strategies, has yet to be systematically evaluated or modeled. To address this gap, this paper introduces WGSR-Bench, the first strategy reasoning benchmark for LLMs using wargame as its evaluation environment. Wargame, a quintessential high-complexity strategic scenario, integrates environmental uncertainty, adversarial dynamics, and non-unique strategic choices, making it an effective testbed for assessing LLMs' capabilities in multi-agent decision-making, intent inference, and counterfactual reasoning. WGSR-Bench designs test samples around three core tasks, i.e., Environmental situation awareness, Opponent risk modeling and Policy generation, which serve as the core S-POE architecture, to systematically assess main abilities of strategic reasoning. Finally, an LLM-based wargame agent is designed to integrate these parts for a comprehensive strategy reasoning assessment. With WGSR-Bench, we hope to assess the strengths and limitations of state-of-the-art LLMs in game-theoretic strategic reasoning and to advance research in large model-driven strategic intelligence.

cs.AI↗

arXiv2022

Comparison principle for stochastic heat equations driven by $\alpha$-stable white noises

For a class of non-linear stochastic heat equations driven by $\alpha$-stable white noises for $\alpha\in(1,2)$ with Lipschitz coefficients, we first show the existence and pathwise uniqueness of $L^p$-valued c\`{a}dl\`{a}g solutions to such a equation for $p\in(\alpha,2]$ by considering a sequence of approximating stochastic heat equations driven by truncated $\alpha$-stable white noises obtained by removing the big jumps from the original $\alpha$-stable white noises. If the $\alpha$-stable white noise is spectrally one-sided, under additional monotonicity assumption on noise coefficients, we prove a comparison theorem on the $L^2$-valued c\`{a}dl\`{a}g solutions of such a equation. As a consequence, the non-negativity of the $L^2$-valued c\`{a}dl\`{a}g solution is established for the above stochastic heat equation with non-negative initial function.

math.PR↗

arXiv2022

Existence of weak solutions to stochastic heat equations driven by truncated $\alpha$-stable white noises with non-Lipschitz coefficients

We consider a class of stochastic heat equations driven by truncated $\alpha$-stable white noises for $1<\alpha<2$ with noise coefficients that are continuous but not necessarily Lipschitz and satisfy globally linear growth conditions. We prove the existence of weak solution, taking values in two different spaces, to such an equation using a weak convergence argument on solutions to the approximating stochastic heat equations. For $1<\alpha<2$ the weak solution is a measure-valued c\`{a}dl\`{a}g process. However, for $1<\alpha<5/3$ the weak solution is a c\`{a}dl\`{a}g process taking function values, and in this case we further show that for $0<p<5/3$ the uniform $p$-th moment for $L^p$-norm of the weak solution is finite, and that the weak solution is uniformly stochastic continuous in $L^p$ sense and satisfies a flow property.

math.PR↗