arXiv · arXiv q-fin · 2022
With the emergence of decentralized finance, new trading mechanisms called Automated Market Makers have appeared. The most popular Automated Market Makers are Constant Function Market Makers. They have been studied both theoretically and empirically. In particular, the concept of impermanent loss has emerged and explains part of the profit and loss of liquidity providers in Constant Function Market Makers. In this pa…
Philippe Bergault, Louis Bertucci, David Bouba, Olivier Guéant
arXiv · arXiv q-fin · 2023
We establish innovative liquidity premium measures, and construct liquidity-adjusted return and volatility to model assets with extreme liquidity, represented by a portfolio of selected crypto assets, and upon which we develop a set of liquidity-adjusted ARMA-GARCH/EGARCH models. We demonstrate that these models produce superior predictability at extreme liquidity to their traditional counterparts. We provide empiric…
Qi Deng, Zhong-guo Zhou
arXiv · arXiv q-fin · 2025
Considering the continuous-time Mean-Variance (MV) portfolio optimization problem, we study a regime-switching market setting and apply reinforcement learning (RL) techniques to assist informed exploration within the control space. We introduce and solve the Exploratory Mean Variance with Regime Switching (EMVRS) problem. We also present a Policy Improvement Theorem. Further, we recognize that the widely applied Temp…
Yuling Max Chen, Bin Li, David Saunders
arXiv · arXiv · 2022
We study the necessary and sufficient conditions under which the Mean-Variance Criterion (MVC) is equivalent to the Maximum Expected Utility Criterion (MEUC), for two lotteries. Based on Chamberlain (1983), we conclude that the MVC is equivalent to the Second-order Stochastic Dominance Rule (SSDR) under any symmetric Elliptical distribution. We then discuss the work of Schuhmacher et al. (2021). Although their theore…
George Samartzis, Nikitas Pittis
arXiv · arXiv q-fin · 2015
In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered mean-variance subject at any point in time. We get explicit trading strategies in the basic model and when random pricing signals are incorporated. When we consider stochastic liquidity and…
Jia-Wen Gu, Mogens Steffensen
arXiv · arXiv q-fin · 2025
In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we parameterise trading strategies as functions in a reproducing kernel Hilbert space (RKHS), enabling a flexible and non-Markovian approach to optimal portfolio problems. We compare this with…
Owen Futter, Nicola Muca Cirone, Blanka Horvath
arXiv · arXiv q-fin · 2019
The portfolio optimisation problem, first raised by Harry Markowitz in 1952, has been a fundamental and central topic to understanding the stock market and making decisions. There has been plenty of works contributing to development of the mean-variance optimisation (MVO) so far. In this paper, one kind of them, namely, dynamic mean-variance optimisation (DMVO) is mainly discussed. One can apply either precommitment …
Xiang Meng
arXiv · arXiv · 2026
The mean-variance model remains the most prevalent investment framework, built on diversification principles. However, it consistently struggles with estimation errors in expected returns and the covariance matrix, its core parameters. To address this concern, this research evaluates the performance of mean variance (MV) and global minimum-variance (GMV) models across various shrinkage estimators designed to improve …
Rupendra Yadav, Amita Sharma, Aparna Mehra
arXiv · arXiv q-fin · 2024
This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or short positions on options. Utilizing SPY options data recorded in five-minute intervals over a one-month period, we calculate key metrics such as Option Greeks and implied volati…
Sid Bhatia
arXiv · arXiv q-fin · 2023
The time proximity of trades across stocks reveals interesting topological structures of the equity market in the United States. In this article, we investigate how such concurrent cross-stock trading behaviors, which we denote as co-trading, shape the market structures and affect stock price co-movements. By leveraging a co-trading-based pairwise similarity measure, we propose a novel method to construct dynamic net…
Yutong Lu, Gesine Reinert, Mihai Cucuringu
arXiv · arXiv · 2022
Traditional portfolio management methods can incorporate specific investor preferences but rely on accurate forecasts of asset returns and covariances. Reinforcement learning (RL) methods do not rely on these explicit forecasts and are better suited for multi-stage decision processes. To address limitations of the evaluated research, experiments were conducted on three markets in different economies with different ov…
Ruan Pretorius, Terence van Zyl
arXiv · arXiv · 2019
Financial portfolio management is one of the problems that are most frequently encountered in the investment industry. Nevertheless, it is not widely recognized that both Kelly Criterion and Risk Parity collapse into Mean Variance under some conditions, which implies that a universal solution to the portfolio optimization problem could potentially exist. In fact, the process of sequential computation of optimal compo…
Yoshiharu Sato
arXiv · arXiv · 2026
Quantum combinatorial optimization offers theoretical advantages for complex financial modeling, but physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology. This study presents a hardware benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA)…
Prashik N. Somkuwar, K. Srinivasan, G. Raghavan
arXiv · arXiv · 2024
Apart from assessing individual asset performance, investors in financial markets also need to consider how a set of firms performs collectively as a portfolio. Whereas traditional Markowitz-based mean-variance portfolios are widespread, network-based optimisation techniques offer a more flexible tool to capture complex interdependencies between asset values. However, most of the existing studies do not contain firms…
Kamesh Korangi, Christophe Mues, Cristián Bravo
arXiv · arXiv · 2023
This paper proposes a unified adaptive portfolio-management framework that combines factor-based view generation, Black-Litterman (BL) posterior estimation, EWMA covariance estimation, and mean-variance optimization. The key mechanism is a dynamic sliding window that adjusts the estimation horizon according to realized portfolio volatility, thereby updating factor estimates, BL posterior expected returns, and portfol…
Chi-Lin Li, Chung-Han Hsieh
arXiv · arXiv · 2022
The random values and volumes of consecutive trades made at the exchange with shares of security determine its mean, variance, and higher statistical moments. The volume weighted average price (VWAP) is the simplest example of such a dependence. We derive the dependence of the market-based variance and 3rd statistical moment of prices on the means, variances, covariances, and 3rd moments of the values and volumes of …
Victor Olkhov
arXiv · arXiv · 2019
This paper investigates the hedging performance of pegged foreign exchange market in a regime switching (RS) model introduced in a recent paper by Drapeau, Wang and Wang (2019). We compare two prices, an exact solution and first order approximation and provide the bounds for the error. We provide exact RS delta, approximated RS delta as well as mean variance hedging strategies for this specific model and compare thei…
Samuel Drapeau, Yunbo Zhang
arXiv · arXiv · 2018
Financial markets change their behaviours abruptly. The mean, variance and correlation patterns of stocks can vary dramatically, triggered by fundamental changes in macroeconomic variables, policies or regulations. A trader needs to adapt her trading style to make the best out of the different phases in the stock markets. Similarly, an investor might want to invest in different asset classes in different market regim…
Sonam Srivastava, Ritabratta Bhattacharya