arXiv subjects

Wenyuan Li

Publications and source records attributed to Wenyuan Li.

At least 19 recordsLinked to original sources

arXiv2026

Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery

We present Eureka, a task-conditioned Meta-Agent architecture that compiles long-horizon tasks into dynamic obligation graphs with explicit acceptance semantics. During execution, Eureka forms Macro-Agents with specialized state, memory, operators, tools, verifiers, and local topology via receding-horizon planning, architecture promotion, and minimal-sufficient compilation. When bottlenecks recur, cost-benefit-gated evolution updates the local architecture under constraints. Theoretically, we establish results on regret, planning invalidation, amortization, subtree interfaces, serializability, and verification. Experimentally, Eureka completes 170/170 recursive tasks and generates 3,948 certificates with no false acceptances. Active context compresses median input from 9,490 to 4,005 tokens; incremental processing avoids 65.38% recomputation across 12,000 tasks; 16,000 concurrent executions serialize consistently. The same Meta-Agent instantiates a Theory-Discovery Agent and a Math/Conjecture Agent. The former yields structural results in quantum-process and spacetime theory. The latter identifies bottlenecks in Riemann Hypothesis research and advances a positivity certificate for Suzuki's localized Weil quadratic form to 0 < a <= 69/200 = 0.345, reaching ~99.55% of (log 2)/2. These results suggest that scientific-agent capability depends not only on the base model but on whether an architecture can be formed to match the task's cognitive structure.

cs.AI↗

arXiv2026

Constrained portfolio optimization in a life-cycle model: A deep pricing kernel approach

This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize their consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, with the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint as special cases. We build the artificial markets to solve this problem by manipulating the compensated drift terms of the underlying assets to meet the trading constraints. By dual transform, we propose a deep pricing kernel approach to compute tight lower and upper bounds for the primal problem, which can be used when the value function lacks an explicit solution due to the pricing kernel's conditional expectation. Finally, we conclude that when considering the trading constraints, the individual will reduce their consumption, demand for life insurance and annuities, and wealth levels due to the restricted market.

q-fin.PM↗

arXiv2026

Optimal Life Insurance Decision in Mean-Variance DC Management with Mortality Improvements

This paper studies the investment and insurance strategies of defined-contribution (DC) pension plans under the mean-variance framework. We consider a stochastic environment with time-varying interest rates, contributions, and mortality risk. The DC plan members are allowed to decide their bond and stock allocations, as well as their life insurance coverage. Adopting the martingale approach, we derive the closed-form optimal strategies and the mean-variance efficient frontier. Further numerical analysis investigates how mortality improvements affect investment and insurance decisions, as well as the sensitivity of the optimal decision to market parameters. Our analysis suggests that longevity raises expectations of future contributions, allowing pension members to adopt a less risky investment strategy. Meanwhile, insurance strategy shifts toward early adulthood to protect the high value of future income and decreases significantly at later ages. Moreover, we conduct sensitivity analyses on the target expected wealth, market price of risk, and contribution growth. These findings provide practical guidance for pension members on investment and offer insights for the design of DC pension plans.

q-fin.PM↗

arXiv2026

Non-concave Corporate Management with Option Incentives under Value-at-Risk Constraint

This article studies a dynamic corporate risk management problem by considering the decision-making of risk-averse managers who exert costly effort and select project risk. We study how a Value-at-Risk (VaR) constraint affects managerial decisions and the distribution of firm value when the manager's objective is non-concave with a fixed salary and options. By the concavification technique, we analyze the optimal terminal firm value on the concave envelope of the objective function. Applying the quantile formulation and the martingale approach, we can derive explicit solutions for optimal effort, terminal firm value, and project choice. The optimal terminal firm value can be divided into nine cases by carefully discussing the choices of VaR floor and tail probability. Compared with the benchmark case, we find that a VaR manager will smooth terminal firm value across states, reducing it in good states while supporting it in adverse states. Moreover, a VaR requirement generally improves downside protection and reduces bankruptcy probability when the VaR floor is low or moderate. However, when the VaR floor is sufficiently high, it can increase bankruptcy probability and induce gambling-for-recovery behavior in adverse states. Our sensitivity analysis indicates that greater managerial effort uniformly improves firm value. Moreover, more incentive options make managers more responsible, leading to a smoother terminal firm value across states. In contrast, a high fixed salary makes the manager less responsible and ultimately causes a more dispersed firm value.

q-fin.MF↗

arXiv2026

Time-consistent catastrophe risk management under the path-dependent effects

This paper investigates optimal investment and insurance strategies under a mean-variance criterion with path-dependent effects. We use a rough volatility model with a power kernel and a Hawkes process with a modified Omori kernel (a power kernel) to capture the market's path dependence. By extending the functional Ito calculus to the mixed fractional Brownian-Hawkes process, we derive the corresponding path-dependent extended Hamilton-Jacobi-Bellman equation and solve its explicit solution. For numerical analysis, we first calibrate the Hawkes process with the Wenchuan earthquake data, the most devastating earthquake in China. We find that the power kernel outperforms the exponential one in fitting the earthquake intensity. Our numerical results reveal that the path-dependent effect strongly depends on the horizon length. For the investment strategy, the individual is more risk-seeking when considering the rougher volatility in the short horizon, but more risk-averse at the beginning of the long horizon. For the insurance strategy, a faster decay in intensity increases individuals' demand for catastrophe insurance in the short horizon, but decreases initially in the long horizon. However, we find that the horizon effect may disappear when the shift parameter in the modified Omori kernel approaches zero or exceeds one. Our findings indicate that ignoring path-dependent effects would lead to significant underinsurance and highlight its importance in catastrophe risk management.

q-fin.RM↗

arXiv2026

Option pricing under non-Markovian stochastic volatility models: A deep signature approach

This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices depend not only on the current state, but also on the entire historical path of the process. To overcome these difficulties, we reformulate the asset dynamics as a rough stochastic differential equation and then represent the rough paths via linear or non-linear combinations of time-extended Brownian motion signatures. This representation transforms a rough stochastic differential equation to a classical stochastic differential equation, allowing the application of standard analytical tools. We propose a deep signature approach for both linear and nonlinear representations and rigorously prove the convergence of the algorithm. Numerical examples demonstrate the effectiveness of our approach for both Markovian and non-Markovian volatility models, offering a theoretically grounded and computationally efficient framework for option pricing.

q-fin.MF↗

arXiv2026

Image Encryption via Data-Identified Discrete Chaotic Maps

In this work, we propose a data-driven image encryption framework that identifies chaotic maps directly from data using the SINDy-PI algorithm. Unlike conventional encryption schemes relying on predefined maps, our method learns the full explicit dynamics -- including cross-terms and higher-order nonlinearities -- from observational data. The validity of this approach is verified on three distinct chaotic systems: the H{é}non map, the three-dimensional logistic map, and the piecewise-linear Lozi map, demonstrating its generality. The encryption key consists solely of initial conditions; the map structure itself becomes data-dependent, introducing an extra layer of security. Moreover, even when the initial conditions are fixed, different training data (e.g., with a tiny noise seed) lead to slightly different maps, which produce completely different ciphertexts (NPCR $\approx 99.6\%$, UACI $\approx 33.5\%$). Numerical experiments on the H{é}non system show near-ideal information entropy ($\approx 8$ bits), negligible inter-pixel correlation, and extreme sensitivity to initial conditions: a perturbation of $10^{-16}$ causes total decryption failure. The scheme resists both differential and statistical attacks, with NPCR and UACI values matching theoretical ideals. Our results establish a new paradigm for chaos-based cryptography beyond fixed maps.

cs.CR↗

arXiv2026

Predictive but Not Plannable: RC-aux for Latent World Models

A latent world model may achieve accurate short-horizon prediction while still inducing a latent space that is poorly aligned with planning. A key issue is spatiotemporal mismatch: these models are often trained with local predictive supervision, but deployed for long-horizon goal-directed search in latent spaces where Euclidean distance may not reflect what is reachable within a finite action budget. We present the Reachability-Correction auxiliary objective (RC-aux), a lightweight correction for this mismatch in reconstruction-free latent world models. RC-aux keeps the world-model backbone unchanged and adds planning-aligned supervision along two axes. Along the time axis, multi-horizon open-loop prediction trains the model beyond one-step consistency. Along the space axis, budget-conditioned reachability supervision, together with temporal hard negatives, encourages the latent space to distinguish states that are eventually reachable from those reachable within the current planning horizon. At test time, the learned reachability signal can also be used by a reachability-aware planner to favor trajectories that are both goal-directed and attainable under the available budget. We instantiate RC-aux on LeWorldModel and evaluate it under both continuation-training and matched-from-scratch settings. Across goal-conditioned pixel-control tasks and a LIBERO-Goal extension, RC-aux improves LeWM-style planning with modest additional cost. These results suggest that planning with latent world models depends not only on predictive accuracy, but also on whether the learned representation encodes the temporal and geometric structure required by downstream search. The code is available at https://github.com/Guang000/RC-aux.

cs.LG↗

arXiv2026

Valuation of variable annuities under the Volterra mortality and rough Heston models

This paper investigates the valuation of variable annuity contracts with an early surrender option under non-Markovian models. Moreover, policyholders are provided with guaranteed minimum maturity and death benefits to protect against the downside risk. Unlike the existing literature, our variable annuity account value is linked to two non-Markovian processes: an equity index modeled by a rough Heston model and a force of mortality following a Volterra-type stochastic model. In this case, the early surrender feature introduces an optimal stopping problem where continuation values depend on the entire path history, rendering traditional numerical methods infeasible. We develop a deep signature Least Squares Monte Carlo approach to learn optimal surrender strategies on a discretized time grid. To mitigate the curse of dimensionality arising from the path-dependent model, we use truncated rough-path signatures to encode the historical paths and approximate the continuation values using a neural network. Numerically, we find that the fair fee increases with the Hurst parameters of both the stock volatility and the force of mortality. Finally, a convergence proof is provided to further support the stability of our method.

q-fin.CP↗

arXiv2026

LLM Framework for Discovering Major Mathematical Conjectures: AI's Quest for the Next Riemann Hypothesis

Major mathematical conjectures still depend heavily on expert intuition, so a unified method for the systematic generation and validation of conjectures with substantial mathematical potential remains unavailable. We present a three stage pipeline for major conjecture discovery, with region search from explicit local evidence modules, reflective validation for foundationality, novelty, and potential significance, and formal validation in Lean 4 and Mathlib. The objective is the discovery of mathematical problems with high problem taste, namely problems whose proofs could reorganize the language of a research area and provide durable help to human mathematical research. Experiments on twenty candidates showstable passage from natural language to formal checks, with twenty out of twenty candidates passing Lean parsing and type checking, twenty out of twenty candidates not directly absorbed by exact?,twenty out of twenty candidates not automatically discharged by aesop, and no explicit duplicates or near duplicates.

cs.AI↗

arXiv2026

DynamicVis: Dynamic Visual Perception for Efficient Remote Sensing Foundation Models

The advancement of RS technology has enabled high-resolution Earth observation; however, interpreting these images using modern VFMs remains a significant challenge. Unlike object-centric natural images, RS imagery is fundamentally characterized by extreme target sparsity and massive spatial redundancy. Key objects of interest (e.g., ships, vehicles) often occupy less than 1% of the spatial extent, surrounded by vast, target-free backgrounds. Existing VFMs predominantly rely on uniform dense processing (e.g., ViTs) and pixel-reconstruction pre-training paradigms (e.g., MAE). These approaches inherently waste substantial computational capacity on modeling redundant backgrounds and inadvertently dilute the feature representations of small, sparse targets. To bridge this structural misalignment, we propose DynamicVis, a visual foundation model explicitly tailored to the sparse nature of RS imagery. Architecturally, DynamicVis introduces a Dynamic Region-Aware SSM that bypasses uniform computation. It adaptively routes and incrementally models only task-relevant, high-salience tokens while employing a parameter-free integration for background context, drastically reducing the complexity of processing ultra-long 2D token sequences ($\sim$100,000). Crucially, to equip the network with robust spatial-selection capabilities, we propose a novel Region-Level Meta-Embedding Multi-Instance Learning (MIL) pre-training paradigm. Trained on a million-scale dataset, this paradigm explicitly disentangles sparse foreground instances from dense backgrounds in the latent semantic space, overcoming the semantic ambiguity of conventional pixel-reconstruction methods. Extensive evaluations across nine diverse downstream tasks reveal that DynamicVis exhibits exceptional efficacy, particularly dominating in sparse-target and instance-level perception tasks (e.g., small object detection, and change detection).

cs.CV↗

arXiv2026

UniTS: Unified Spatio-Temporal Generative Model for Remote Sensing

One of the primary objectives of satellite remote sensing is to capture the complex dynamics of the Earth environment, which encompasses tasks such as reconstructing continuous cloud-free image sequences, detecting land cover changes, and forecasting future surface evolution. However, existing methods typically require specialized models tailored to different tasks, and lack a general framework that can address these multi-level tasks from a unified perspective. In this paper, we propose a Unified Spatio-Temporal Generative Model (UniTS), which integrates several long-separated core tasks, including time series reconstruction, time series cloud removal, time series semantic change detection, and time series forecasting. Based on the flow matching generative paradigm, UniTS constructs a deterministic evolution path from noise to targets under the guidance of task-specific conditions, achieving unified modeling of spatiotemporal representations for multi-level tasks. The UniTS architecture consists of a diffusion transformer with spatiotemporal blocks, where we design an Adaptive Condition Injector (ACor) to enhance the model's conditional perception of multimodal inputs, enabling high-quality controllable generation. Additionally, we design a Spatiotemporal-aware Modulator (STM) to improve the ability of spatiotemporal blocks to capture complex spatiotemporal dependencies. It substantially outperforms existing specialized models, particularly under challenging conditions such as severe cloud contamination, modality absence, and forecasting complex phenological variations.

cs.CV↗

arXiv2026

Positive microlocal holonomies are globally regular

We establish a geometric criterion for local microlocal holonomies to be globally regular on the moduli space of Lagrangian fillings. This local-to-global regularity result holds for arbitrary Legendrian links and it is a key input for the study of cluster structures on such moduli spaces. Specifically, we construct regular functions on derived moduli stacks of sheaves with Legendrian microsupport by studying the Hochschild homology of the associated dg-categories via relative Lagrangian skeleta. In this construction, a key geometric result is that local microlocal merodromies along positive relative cycles in Lagrangian fillings yield global Hochschild 0-cycles for these dg-categories.

math.SG↗

arXiv2026

AgriFM: A Multi-source Temporal Remote Sensing Foundation Model for Agriculture Mapping

Accurate crop mapping fundamentally relies on modeling multi-scale spatiotemporal patterns, where spatial scales range from individual field textures to landscape-level context, and temporal scales capture both short-term phenological transitions and full growing-season dynamics. Transformer-based remote sensing foundation models (RSFMs) offer promising potential for crop mapping due to their innate ability for unified spatiotemporal processing. However, current RSFMs remain suboptimal for crop mapping: they either employ fixed spatiotemporal windows that ignore the multi-scale nature of crop systems or completely disregard temporal information by focusing solely on spatial patterns. To bridge these gaps, we present AgriFM, a multi-source remote sensing foundation model specifically designed for agricultural crop mapping. Our approach begins by establishing the necessity of simultaneous hierarchical spatiotemporal feature extraction, leading to the development of a modified Video Swin Transformer architecture where temporal down-sampling is synchronized with spatial scaling operations. This modified backbone enables efficient unified processing of long time-series satellite inputs. AgriFM leverages temporally rich data streams from three satellite sources including MODIS, Landsat-8/9 and Sentinel-2, and is pre-trained on a global representative dataset comprising over 25 million image samples supervised by land cover products. The resulting framework incorporates a versatile decoder architecture that dynamically fuses these learned spatiotemporal representations, supporting diverse downstream tasks. Comprehensive evaluations demonstrate AgriFM's superior performance over conventional deep learning approaches and state-of-the-art general-purpose RSFMs across all downstream tasks. Codes will be available at https://github.com/flyakon/AgriFM.

cs.CV↗

arXiv2025

Monopoly Pricing of Weather Index Insurance

This study models the monopoly pricing of weather index insurance as a Bowley-type sequential game involving a profit-maximizing insurer (leader) and a farmer (follower). The farmer chooses an insurance payoff to minimize a convex distortion risk measure, while the insurer anticipates this best response and selects a premium principle and its parameters to maximize profit net of administrative costs. For the insurer, we adopt three different premium-principle parameterizations: (i) an expected premium with a single risk-loading factor, (ii) a two-parameter distortion premium based on a power transform, and (iii) a fully flexible pricing kernel drawn from the general Choquet integral representation with nondecreasing distortions. For the farmer, we model index payoffs using neural networks and compare solutions under fully connected architectures with those under convolutional neural networks (CNNs). We solve the game using a penalized bilevel programming algorithm that employs a function-value-gap penalty and delivers convergence guarantees without requiring the lower-level objective to be strongly convex. Based on Iowa's soybean yields and high-dimensional PRISM weather data, we find that CNN-based designs yield smoother, less noisy payoffs that reduce basis risk and push insurer profits closer to indemnity insurance levels. Moreover, expanding pricing flexibility from a single loading to a two-parameter distortion premium, and ultimately to a flexible pricing kernel, systematically increases equilibrium profits.

q-fin.RM↗

arXiv2025

Microsheaf composition of Lagrangian correspondences

In exact symplectic manifolds whose Liouville flow is gradientlike for a proper Morse function, one can associate conic microsheaves to eventually conic exact Lagrangians. Here we study how this 'microsheaf quantization' interacts with composition of Lagrangian correspondences. In particular: these operations commute when the composition is embedded. As an illustration, we show that Lie groups of exact symplectomorphisms act on microsheaf categories. The key technical advance is a version 'in families' of the gappedness criterion for commuting nearby cycles past tensor or Hom.

math.SG↗

arXiv2025

Decoupled Audio-Visual Dataset Distillation

Audio-Visual Dataset Distillation aims to compress large-scale datasets into compact subsets while preserving the performance of the original data. However, conventional Distribution Matching (DM) methods struggle to capture intrinsic cross-modal alignment. Subsequent studies have attempted to introduce cross-modal matching, but two major challenges remain: (i) independently and randomly initialized encoders lead to inconsistent modality mapping spaces, increasing training difficulty; and (ii) direct interactions between modalities tend to damage modality-specific (private) information, thereby degrading the quality of the distilled data. To address these challenges, we propose DAVDD, a pretraining-based decoupled audio-visual distillation framework. DAVDD leverages a diverse pretrained bank to obtain stable modality features and uses a lightweight decoupler bank to disentangle them into common and private representations. To effectively preserve cross-modal structure, we further introduce Common Intermodal Matching together with a Sample-Distribution Joint Alignment strategy, ensuring that shared representations are aligned both at the sample level and the global distribution level. Meanwhile, private representations are entirely isolated from cross-modal interaction, safeguarding modality-specific cues throughout distillation. Extensive experiments across multiple benchmarks show that DAVDD achieves state-of-the-art results under all IPC settings, demonstrating the effectiveness of decoupled representation learning for high-quality audio-visual dataset distillation. Code will be released.

cs.CV↗

arXiv2025

Mean Field Analysis of Mutual Insurance Market

A mutual insurance company (MIC) is a type of consumer cooperative owned by its policyholders. By purchasing insurance from an MIC, policyholders effectively become member-owners of the company and are entitled to a share of the surplus, which is determined by their own collective claims and premium contributions. This sharing mechanism creates an interactive environment in which individual insurance strategies are influenced by the actions of others. Given that mutual insurers account for nearly one-third of the global insurance market, the analysis of members' behavior under such a sharing mechanism is of both practical and theoretical importance. This article presents a first dynamic study of members' behavior in the prevalent mutual insurance market under the large-population limit. With members' wealth processes depending on the law of the insurance strategies, we model the surplus-sharing mechanism using an extended mean field game (MFG) framework and address the fundamental question of how strategic interactions in this setting influence individual decisions. Mathematically, we establish the global-in-time existence and uniqueness of the mean field forward-backward stochastic differential equation (MF-FBSDE) characterizing the Nash equilibrium strategy, employing techniques to accommodate realistic insurance constraints. Computationally, we develop a modified deep BSDE algorithm capable of solving the extended MFG problem with an additional fixed-point structure on the control. Utilizing this scheme, we examine how structural features of the MIC's design, such as the composition of risk classes and surplus-sharing proportions, reshape members' decisions and wealth through collective interactions, underscoring the central role of these mechanisms in MICs.

q-fin.RM↗