Huyen Pham

Fabien Guilbaud, Huyen Pham

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders

Huyen Pham, Bilhanan Silverajan

The growing adoption of edge computing has created an increasing need for workloads capable of operating under strict resource and energy constraints. Neuromorphic computing, and spiking neural networks (SNNs) in particular, offers an energy-efficient alternative to conventional machine learning through event-driven computation. However, how SNN workloads behave when deployed within modern container orchestration frameworks, especially in edge environments, remains largely unexplored. This paper investigates the feasibility of deploying and orchestrating SNN workloads in a virtual edge environment using Kubernetes, focusing on end-to-end latency, throughput, classification accuracy, infrastructure overhead, and runtime behavior under concurrent load. Experiments were conducted on a single-node K3d cluster running on a Windows 11 host with WSL2 and Docker Desktop. The results show that SNN workloads are highly sensitive to resource availability. Restricting CPU to 0.5 cores increased median latency by 47.6x and reduced throughput by 49x, while the most constrained configuration failed due to insufficient memory. Classification accuracy remained stable across all working configurations. From an orchestration perspective, K3d successfully deployed and scaled SNN workloads, though its default round-robin routing policy introduced significant tail latency under replica scaling, highlighting a mismatch between stateless load-balancing assumptions and long-running inference workloads. Overall, this study provides a baseline for deploying neuromorphic workloads in containerized edge environments and highlights the importance of resource provisioning and orchestration configuration. Future work should explore improved routing strategies, memory optimization, and validation on physical edge hardware.

Zhe Fei, Mehmet Yigit Turali, Shreyas Rajesh et al.

Harmonizing medication data across Electronic Health Record (EHR) systems is a persistent barrier to monitoring medications for opioid use disorder (MOUD). In heterogeneous EHR systems, key prescription attributes are scattered across differently formatted fields and freetext notes. We present a practical framework that customizes open source large language models (LLMs), including Llama, Qwen, Gemma, and MedGemma, to extract a unified set of MOUD prescription attributes (prescription date, drug name, duration, total quantity, daily quantity, and refills) from heterogeneous, site specific data and compute a standardized metric of medication coverage, \emph{MOUD days}, per patient. Our pipeline processes records directly in a fixed JSON schema, followed by lightweight normalization and cross-field consistency checks. We evaluate the system on prescription level EHR data from five clinics in a national OUD study (25{,}605 records from 1{,}257 patients), using a previously annotated benchmark of 10{,}369 records (776 patients) as the ground truth. Performance is reported as coverage (share of records with a valid, matchable output) and record-level exact-match accuracy. Larger models perform best overall: Qwen2.5-32B achieves \textbf{93.4\%} coverage with \textbf{93.0\%} exact-match accuracy across clinics, and MedGemma-27B attains \textbf{93.1\%}/\textbf{92.2\%}. A brief error review highlights three common issues and fixes: imputing missing dosage fields using within-drug norms, handling monthly/weekly injectables (e.g., Vivitrol) by setting duration from the documented schedule, and adding unit checks to prevent mass units (e.g., ``250 g'') from being misread as daily counts. By removing brittle, site-specific ETL and supporting local, privacy-preserving deployment, this approach enables consistent cross-site analyses of MOUD exposure, adherence, and retention in real-world settings.

Achref Bachouch, Côme Huré, Nicolas Langrené et al.

This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [EHJ17] and on quadratic backward stochastic differential equations as in [CR16]. We also performed tests on low-dimension control problems such as an option hedging problem in finance, as well as energy storage problems arising in the valuation of gas storage and in microgrid management. Numerical results and comparisons to quantization-type algorithms Qknn, as an efficient algorithm to numerically solve low-dimensional control problems, are also provided; and some corresponding codes are available on https://github.com/comeh/.

Huyen Pham, Xavier Warin, Maximilien Germain

We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient at previous step. This methodology extends to the fully nonlinear case the approach recently proposed in \cite{HPW19} for semi-linear PDEs. Numerical tests illustrate the performance and accuracy of our method on several examples in high dimension with nonlinearity on the Hessian term including a linear quadratic control problem with control on the diffusion coefficient, Monge-Amp{è}re equation and Hamilton-Jacobi-Bellman equation in portfolio optimization.