Singular Perturbation Expansion for Utility Maximization with Order-$\epsilon$ Quadratic Transaction Costs

Andrew Papanicolaou; Shiva Chandra

Home/Archive/arXiv

arXiv · 1910.06463

Singular Perturbation Expansion for Utility Maximization with Order-$\epsilon$ Quadratic Transaction Costs

Andrew Papanicolaou·Shiva Chandra

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $\epsilon$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of $\sqrt\epsilon$. In this paper we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

Explore related subjects

q-fin.TR q-fin.PM

Keep this discovery

BibTeX RIS

Andrew Papanicolaou, Shiva Chandra. 2019-10-14. Singular Perturbation Expansion for Utility Maximization with Order-$\epsilon$ Quadratic Transaction Costs. https://arxiv.org/abs/1910.06463

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Deep Learning of Robust Market Making under Regime-Switching Order Flow

Classical market-making strategies based on stochastic control, such as the Avellaneda-Stoikov and the Gu\'{e}ant-Lehalle-Fernandez-Tapia (GLFT) extension, provide closed-form quoting rules, but rest on assumptions that break down at realistic microstructure timescales. One of them is that order flow is stationary, while empirical evidence points to the existence of regimes, possibly associated with algorithmic execution of metaorders. In this case, existing methods provide negative PnL. In this paper, we develop a deep reinforcement-learning market maker (RLMM) - a Rainbow-style distributional DQN (C51) which is calibrated and tested in a zero-intelligence limit order book. We find that, in the stationary setting, RLMM outperforms GLFT across the entire observed risk-return frontier. The RLMM is more robust to flow asymmetry than GLFT, but, like any stationarily trained strategy, it still suffers large drawdowns from inventory saturation under persistent directional imbalance. Augmenting the state of RLMM with two auxiliary signals - a Bayesian online change-point filter over the directional flow bias and a queue-adjusted quote-exposure imbalance -restores profitability. A final scenario-bandit step that reweights low-return regime scenarios further improves performance under random-persistence and correlated-direction stress.

q-fin.TR↗

arXiv2026

dexamine: A Python package for Uniswap event data on Ethereum

Decentralized exchanges record trading and liquidity provision on public blockchains, but empirical analysis requires interpreting these records and linking them to execution metadata. dexamine is a Python package that parses Uniswap v2 and v3 events on Ethereum. It converts transaction receipt logs into observations of trades and liquidity changes, with token quantities, pool state, transaction order, and gas information. The package separates data retrieval, contract metadata, protocol interpretation, and output construction. The repository provides recorded Ethereum responses and an offline reproducible example, and version 1 has been used to construct data for an empirical study of price discovery in decentralized markets.

q-fin.TR↗

arXiv2026

The Double-Edged Sword of Short-Selling Bans

We develop a theoretical model that endogenizes the regulator's decision to impose short-selling bans to prevent large stock price declines. Empirically, we test the model's predictions using the cross-sectional variation in short-selling restrictions implemented across European countries in 2020. Consistent with our model, we find that bans had a detrimental effect on liquidity and failed to support the average price levels, but were effective in limiting large price drawdowns. Finally, we show that the effectiveness of the bans depends on the share of informed stockholders, a central variable in our framework, thus informing the design of more effective regulatory responses.

q-fin.TR↗