arXiv subjects

Daria Sakhanda

Publications and source records attributed to Daria Sakhanda.

3 recordsLinked to original sources

arXiv2026

Stochastic Optimal Control of Hawkes Jump-Diffusion Systems

This paper is devoted to developing a framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. Building on the Poisson point process formulation studied in arXiv:2511.13568, we extend the model to disasters driven by a marked Hawkes process, allowing past disasters to temporarily increase the likelihood of subsequent shocks. Our work focuses on a subcritical Markovian Hawkes specification, in which the state space is augmented by the self-excitation component of disaster risk. We establish the well-posedness and nonexplosion of the resulting controlled Hawkes dynamics. Using the Hamilton-Jacobi-Bellman characterization of the corresponding Poisson control problem, we obtain quantitative estimates for the Hawkes excitation process and prove, under a small-excitation scaling, that the Hawkes value function converges to its Poisson counterpart as the magnitude of self-excitation vanishes. This provides a rigorous Poisson approximation of the stochastic control problem and quantifies the effect of self-excitation on optimal growth under environmental disaster risk.

math.OC↗

arXiv2025

Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters

This paper is devoted to developing a unified framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. The analysis is based upon a general Poisson point process formulation, leading to non-local Hamilton-Jacobi-Bellman (HJB) equations that admit closed-form candidate solutions and yield a composite state variable capturing exposure to rare shocks. We consider cases where disaster risk is endogenized through a pollution-dependent intensity and, in the more general cases, it also accommodates for state-dependent events of varying magnitude. Our formulation captures how environmental degradation amplifies macroeconomic vulnerability and strengthens incentives for abatement. From a technical perspective, it provides tractable jump-diffusion control problems whose HJB equation decomposes naturally into capital and pollution components under power-type value function.

math.OC↗

arXiv2025

IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 77 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can already solve a significant percentage of research-level questions. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

cs.CL↗