Risk Control

Equilibrium Portfolio Selection under Utility-Variance Analysis of Log Returns in Incomplete Markets ArXiv ID: 2511.05861 “View on arXiv” Authors: Yue Cao, Zongxia Liang, Sheng Wang, Xiang Yu Abstract This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log returns, giving rise to time inconsistency and motivating the search of a time-consistent equilibrium strategy. We characterize the equilibrium via a coupled quadratic backward stochastic differential equation (BSDE) system and establish the existence theory in two special cases: (i)the two Brownian motions driven the price dynamics and the factor process are independent with $ρ= 0$; (ii) the trading strategy is constrained to be bounded. For the general case with correlation coefficient $ρ\neq 0$, we introduce the notion of an approximate time-consistent equilibrium. Employing the solution structure from the equilibrium in the case $ρ= 0$, we can construct an approximate time-consistent equilibrium in the general case with an error of order $O(ρ^2)$. Numerical examples and financial insights are also presented based on deep learning algorithms. ...

Optimization Method of Multi-factor Investment Model Driven by Deep Learning for Risk Control ArXiv ID: 2507.00332 “View on arXiv” Authors: Ruisi Li, Xinhui Gu Abstract Propose a deep learning driven multi factor investment model optimization method for risk control. By constructing a deep learning model based on Long Short Term Memory (LSTM) and combining it with a multi factor investment model, we optimize factor selection and weight determination to enhance the model’s adaptability and robustness to market changes. Empirical analysis shows that the LSTM model is significantly superior to the benchmark model in risk control indicators such as maximum retracement, Sharp ratio and value at risk (VaR), and shows strong adaptability and robustness in different market environments. Furthermore, the model is applied to the actual portfolio to optimize the asset allocation, which significantly improves the performance of the portfolio, provides investors with more scientific and accurate investment decision-making basis, and effectively balances the benefits and risks. ...

Dynamic Grid Trading Strategy: From Zero Expectation to Market Outperformance ArXiv ID: 2506.11921 “View on arXiv” Authors: Kai-Yuan Chen, Kai-Hsin Chen, Jyh-Shing Roger Jang Abstract We propose a profitable trading strategy for the cryptocurrency market based on grid trading. Starting with an analysis of the expected value of the traditional grid strategy, we show that under simple assumptions, its expected return is essentially zero. We then introduce a novel Dynamic Grid-based Trading (DGT) strategy that adapts to market conditions by dynamically resetting grid positions. Our backtesting results using minute-level data from Bitcoin and Ethereum between January 2021 and July 2024 demonstrate that the DGT strategy significantly outperforms both the traditional grid and buy-and-hold strategies in terms of internal rate of return and risk control. ...

MILLION: A General Multi-Objective Framework with Controllable Risk for Portfolio Management ArXiv ID: 2412.03038 “View on arXiv” Authors: Unknown Abstract Portfolio management is an important yet challenging task in AI for FinTech, which aims to allocate investors’ budgets among different assets to balance the risk and return of an investment. In this study, we propose a general Multi-objectIve framework with controLLable rIsk for pOrtfolio maNagement (MILLION), which consists of two main phases, i.e., return-related maximization and risk control. Specifically, in the return-related maximization phase, we introduce two auxiliary objectives, i.e., return rate prediction, and return rate ranking, combined with portfolio optimization to remit the overfitting problem and improve the generalization of the trained model to future markets. Subsequently, in the risk control phase, we propose two methods, i.e., portfolio interpolation and portfolio improvement, to achieve fine-grained risk control and fast risk adaption to a user-specified risk level. For the portfolio interpolation method, we theoretically prove that the risk can be perfectly controlled if the to-be-set risk level is in a proper interval. In addition, we also show that the return rate of the adjusted portfolio after portfolio interpolation is no less than that of the min-variance optimization, as long as the model in the reward maximization phase is effective. Furthermore, the portfolio improvement method can achieve greater return rates while keeping the same risk level compared to portfolio interpolation. Extensive experiments are conducted on three real-world datasets. The results demonstrate the effectiveness and efficiency of the proposed framework. ...