Inventory Management

Option market making with hedging-induced market impact ArXiv ID: 2511.02518 “View on arXiv” Authors: Paulin Aubert, Etienne Chevalier, Vathana Ly Vath Abstract This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker’s quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact. ...

Smart Contract Adoption under Discrete Overdispersed Demand: A Negative Binomial Optimization Perspective ArXiv ID: 2510.05487 “View on arXiv” Authors: Jinho Cha, Sahng-Min Han, Long Pham Abstract Effective supply chain management under high-variance demand requires models that jointly address demand uncertainty and digital contracting adoption. Existing research often simplifies demand variability or treats adoption as an exogenous decision, limiting relevance in e-commerce and humanitarian logistics. This study develops an optimization framework combining dynamic Negative Binomial (NB) demand modeling with endogenous smart contract adoption. The NB process incorporates autoregressive dynamics in success probability to capture overdispersion and temporal correlation. Simulation experiments using four real-world datasets, including Delhivery Logistics and the SCMS Global Health Delivery system, apply maximum likelihood estimation and grid search to optimize adoption intensity and order quantity. Across all datasets, the NB specification outperforms Poisson and Gaussian benchmarks, with overdispersion indices exceeding 1.5. Forecasting comparisons show that while ARIMA and Exponential Smoothing achieve similar point accuracy, the NB model provides superior stability under high variance. Scenario analysis reveals that when dispersion exceeds a critical threshold (r > 6), increasing smart contract adoption above 70% significantly enhances profitability and service levels. This framework offers actionable guidance for balancing inventory costs, service levels, and implementation expenses, highlighting the importance of aligning digital adoption strategies with empirically observed demand volatility. ...

Optimal Quoting under Adverse Selection and Price Reading ArXiv ID: 2508.20225 “View on arXiv” Authors: Alexander Barzykin, Philippe Bergault, Olivier Guéant, Malo Lemmel Abstract Over the past decade, many dealers have implemented algorithmic models to automatically respond to RFQs and manage flows originating from their electronic platforms. In parallel, building on the foundational work of Ho and Stoll, and later Avellaneda and Stoikov, the academic literature on market making has expanded to address trade size distributions, client tiering, complex price dynamics, alpha signals, and the internalization versus externalization dilemma in markets with dealer-to-client and interdealer-broker segments. In this paper, we tackle two critical dimensions: adverse selection, arising from the presence of informed traders, and price reading, whereby the market maker’s own quotes inadvertently reveal the direction of their inventory. These risks are well known to practitioners, who routinely face informed flows and algorithms capable of extracting signals from quoting behavior. Yet they have received limited attention in the quantitative finance literature, beyond stylized toy models with limited actionability. Extending the existing literature, we propose a tractable and implementable framework that enables market makers to adjust their quotes with greater awareness of informational risk. ...

Optimal Dynamic Fees in Automated Market Makers ArXiv ID: 2506.02869 “View on arXiv” Authors: Unknown Abstract Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs. ...

Reinforcement Learning for Corporate Bond Trading: A Sell Side Perspective ArXiv ID: 2406.12983 “View on arXiv” Authors: Unknown Abstract A corporate bond trader in a typical sell side institution such as a bank provides liquidity to the market participants by buying/selling securities and maintaining an inventory. Upon receiving a request for a buy/sell price quote (RFQ), the trader provides a quote by adding a spread over a \textit{“prevalent market price”}. For illiquid bonds, the market price is harder to observe, and traders often resort to available benchmark bond prices (such as MarketAxess, Bloomberg, etc.). In \cite{“Bergault2023ModelingLI”}, the concept of \textit{“Fair Transfer Price”} for an illiquid corporate bond was introduced which is derived from an infinite horizon stochastic optimal control problem (for maximizing the trader’s expected P&L, regularized by the quadratic variation). In this paper, we consider the same optimization objective, however, we approach the estimation of an optimal bid-ask spread quoting strategy in a data driven manner and show that it can be learned using Reinforcement Learning. Furthermore, we perform extensive outcome analysis to examine the reasonableness of the trained agent’s behavior. ...

On Risk-Sensitive Decision Making Under Uncertainty ArXiv ID: 2404.13371 “View on arXiv” Authors: Unknown Abstract This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which are deterministic and others are stochastic. The decision-maker’s cumulative value is updated at each stage, reflecting the outcomes of the chosen alternatives. After formulating this as a stochastic control problem, we delineate the necessary optimality conditions for it. Two illustrative examples from optimal betting and inventory management are provided to support our theory. ...