Abstracts

Dynamic capital allocation with reallocation cost

Ermo Chen Peking University: Traditional static risk capital allocation tools can result in significant capital reallocation costs for institutions over multiple periods due to the drastic fluctuations in allocation results. In order to control these costs, this paper proposes a dynamic capital allocation problem that incorporates reallocation costs into the loss function and uses a dynamic programming framework to optimize the problem. Additionally, the stochastic constraints associated with the full allocation requirement are incorporated into the problem formulation. We obtain an analytical expression for the solution of the proposed problem in a recursive form and demonstrate its performance through numerical simulations. Our results indicate that the solution optimizes the overall loss function, and the reallocation costs are worthwhile considering. Furthermore, our approach strikes an effective balance between addressing current risk profiles and preparing for future ones. This dynamic capital allocation method successfully functions as a risk-based capital allocation tool while preserving the advantage of stable allocation. This is a joint work with Lan WU (PKU).

Periodicity in the optimal liquidation game with a major player

Yufan Chen Peking University: It has been documented that intraday high-frequency trading activities exhibit periodicity. In this article, we provides an explanation for this phenomenon through an optimal liquidation game with a major trader. This framework contains (i) a major trader who is liquidating a large number of shares facing an objective with a periodicity and (ii) a number of minor traders(high-frequency traders (HFTs)) who detect and trade against the liquidator. All the traders interact with each other through their impacts on the price dynamics, and we solve this problem by a mean-field game approach. Our results yield open-loop trading strategies for both major and minor traders, highlighting the periodicity in the optimal strategies of all participants. Moreover, we demonstrate that the presence of minor traders, although without periodic objectives, amplifies the periodicity of trading speed across the entire market. This is a joint work with Lan WU (PKU).

Disclosing and cooling-off: an analysis of insider trading rules

Jun DENG University of International Business and Economics: We analyze two insider-trading regulations recently introduced by the U.S. Securities and Exchange Commission: advance disclosure and "cooling-off period." The former requires an insider to disclose trading plans at adoption, while the latter mandates a delay period before execution. Disclosure increases price efficiency but has mixed welfare implications. If the insider has large liquidity needs, in contrast to the conventional wisdom from "sunshine trading," disclosure can even reduce the welfare of all investors. A longer cooling-off period increases outside investors' welfare but decreases price efficiency. Its implication for the insider's welfare depends on whether the disclosure policy is already in place. This is a joint work with Huifeng Pan(UIBE), Hongjun Yan(DePaul) and Liyan Yang(Toronto).

On optimal time-consistent equilibrium stopping under aggregation of diverse discount rates

Shuoqing DENG The Hong Kong University of Science and Technology: We revisit the collective decision making for a group under diverse discount rates. In the context of optimal stopping, we propose a smooth aggregation preference to incorporate all heterogeneous discount rates and an attitude function reflecting the aggregation weight similar to the smooth ambiguity preference in Klibanoff et al. (2005) when handling the model uncertainty. The optimal stopping problem renders to be time inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent equilibrium stopping polices as fixed points of an operator in the setting of one-dimensional diffusion processes. More importantly, we provide some sufficient conditions on both the underlying models and the attitude function such that the smallest equilibrium attains the optimal equilibrium and the attitude function is equivalent to the linear aggregation rule as of diversity neutral.

Sequential propagation of chaos

Kai DU Fudan University: A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov SDE and BSDE that originally arise as the limit of the mean-field interacting particle system. The weighted empirical measure of this particle system is proved to converge to the law of the McKean-Vlasov process as the system grows. Based on the Wasserstein metric, quantitative propagation of chaos results are obtained. Numerical experiments are implemented to demonstrate the theoretical results.

Optimal execution subject to reservation strategies

Peng GUO Peking University: The paper considers optimal execution problems under classical Almgren-Chriss framework subject to some reservation strategies (RS) as benchmark. The investor is risk-averse with CRRA preference. A relative cost, defined by the difference between the realized cost and benchmark cost given by RS, is considered under utility maximization. Some well-known models and strategies could be included in our framework, with different RS, such as an IS order, a TC order and a VWAP/TWAP order. As an extension of IS order and TC order, we consider the optimal execution with endpoints-only RS and show that the optimal strategy is a linear combination of IS order and TC order. Motivated by endpoints-only RS, piece-wise constant RS is concerned to approximated general RS. Finally, we show that Almgren-Chriss optimal execution problem with general price drift can be solved within our framework. This is a joint work with Xue CHENG (PKU) and Tai-ho WANG (Baruch College, USA)

McKean-Vlasov SDE with branching: the well-posedness and propagation of chaos

Jiazhi KANG The Chinese University of Hong Kong: We study a branching diffusion process with interaction, namely, the McKean-Vlasov or Mean-Field SDE with branching. We establish a wellposedness result, together with a propagation of chaos result, that is, it is the limit of the branching process with large population.

Robust equilibrium strategy for mean-variance portfolio selection

Mengge LI National University of Singapore: The classical mean-variance portfolio selection problem induces time-inconsistent precommited strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach and look for (sub-game perfect Nash) equilibrium strategies, which is solved from the corresponding partial differential equations (PDE) system. In their model, the investor perfectly knows the drift and volatility of the assets. However, in reality investors only have an estimate on them, e.g, a 95% confidence interval. In this case, some literature (e.g., Pham, Wei and Zhou (2022)) derives the optimal precommited strategy under the worst parameters, which is the robust control. The relation between the equilibrium strategy and the PDE system has not been justified when incorporating robust control. In this paper, we consider a general dynamic mean-variance framework and propose a novel definition of the robust equilibrium strategy. Under our definition, a classical solution to the corresponding PDE system implies a robust equilibrium strategy. We then explicitly solve for some special examples.

Upper and lower variances and their applications

Xinpeng LI Shandong University: In this talk, we introduce the notions of upper and lower variances for random variables under multiple probability measures and study the related properties. We also provide high-speed algorithm for the calculation of upper variance. As an application, we consider the \(G\)-VaR model with mean-uncertainty which is used in the financial market.

Convergence analysis on the particle systems with centralized control

Huafu LIAO National University of Singapore: This talk is about the optimization problem of a class of \(N\)-particle systems with centralized control. We establish the regularity results, which is uniform in \(N\), on the HJB equations corresponding to the \(N\)-particle system. The uniform regularity results are obtained by the stochastic maximum principle and the analysis on a Riccati type BSDE. Using the uniform regularity results, we show the convergence of the value functions and the optimal controls as the number \(N\) of particles tends to infinity, where the convergence rates are also given. This talk is based on the joint work with Alpár R. Mészáros from Durham University, Chenchen Mou from CityU and Chao Zhou from NUS.

Regularized mean field optimization with application to neural networks

Zhenjie REN University of Paris Dauphine - PSL: Our recent works on the regularized mean field optimization aim at providing a theoretical foundation for analyzing the efficiency of the training of neural networks, as well as inspiring new training algorithms. In this talk we shall see how different regularizers, such as relative entropy and Fisher information, lead to different gradient flows on the space of probability measures. Besides the gradient flows, we also propose and study alternative algorithms, such as the entropic fictitious play, to search for the optimal weights of neural networks. Each of these algorithms is ensured to have exponential convergence, and we shall highlight their performances in some simple numerical tests.

Explicit positive solutions to \(G\)-heat equations and the application to \(G\)-capacities

Yifan SUN Shandong University: In this talk, I will present a class of explicit positive solutions to \(G\)-heat equations by solving second order nonlinear ordinary differential equations. Based on the positive solutions, we give the sharp order of \(G\)-capacity \(c_{sigma}( [ -\varepsilon,\varepsilon] )\) when \(\varepsilon \rightarrow0\). This talk is based on a joint work with Mingshang Hu.

Multi-dimensional BSDEs with mean reflection

Falei WANG Shandong University: In this talk, we consider multi-dimensional mean reflected backward stochastic differential equations with possibly non-convex reflection domains along inward normal direction, which were introduced by Briand, Elie and Hu in the scalar case. We first apply a fixed-point argument to establish the uniqueness and existence result under an additional bounded condition on the driver. Then, with the help of a priori estimates, we develop a successive approximation procedure to remove the additional bounded condition for the general case. Based on a joint work with Baoyou Qu.

A C1-Itô's formula for flows of semimartingale distributions

Jixin WANG The Chinese University of Hong Kong: We provide an Itô's formula for C1-functionals on the flows of conditional marginal distributions of a continuous semimartingale. This is based on the notion of the weak Dirichlet process, and extends the C1-Itô's formula in Gozzi and Russo (2006) in the context of semimartingales. As a first application, we study a class of McKean-Vlasov optimal control problems, and establish a verification theorem by requiring only C1-regularity of its value function, which is equivalently the (viscosity) solution of the associated HJB master equation.

Itô's formula for flows of measures on semimartingales

Xiaoli WEI Tsinghua University (Shenzhen): We establish Itô's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô's formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques. This general form of Itô's formula enables the derivation of dynamic programming equations and verification theorems for McKean--Vlasov controls with jump diffusions and for McKean--Vlasov mixed regular-singular control problems. This is a joint work with Xin Guo and Huyên Pham.

How does node centrality in a complex network affect prediction?

Yuhong XU Soochow University: In complex financial networks, systemically important nodes usually play crucial roles. Asset price forecasting is important for describing the evolution of a financial network. Naturally, we wonder whether node centrality affects forecasting effectiveness. We consider networks consisting of major global assets and explore how node centrality affects price forecasting by applying a hybrid random forest algorithm. Two counterintuitive phenomena are found: (i) factors with low centrality have better forecasting ability, and (ii) nodes with low centrality can be predicted more accurately in direction. Using the notion of entropy, which measures the quantity of information, we show that factors with low centrality have more useful information and less noise for the forecast asset price than factors with high centrality do. In addition, while predicting a systemically unimportant node, we demonstrate that the other nodes within the network have a higher information rate concerning the forecast asset. Moreover, our research suggests a criterion for factor selection: when predicting an asset price in a complex system, factors with low centrality should be selected rather than only factors with high centrality. Finally, we verify the robustness of our results using an alternative deep learning method.

Continuous time q-learning for McKean-Vlasov control problems

Xiang YU The Hong Kong Polytechnic University: This paper studies the q-learning, recently coined as the continuous-time counterpart of Q-learning by Jia and Zhou (2023), for continuous time Mckean-Vlasov control problems in the setting of entropy-regularized reinforcement learning. In sharp contrast to the single agent's control problem in Jia and Zhou (2023), the mean-field interactions of agents render the definition of q-function more subtle, for which we reveal that two distinct q-functions naturally arise: (i) the q-function (denoted by \(q\)) as the first-order approximation of the Q-function that can be learnt by a weak martingale condition involving test policies; and (ii) the essential q-function (denoted by \(q_e\)) that is employed in the characterization of the optimal policy and the policy improvement iterations. We show that two q-functions are related via an integral representation under all test policies. When the population distribution is not directly observable, we also investigate the decoupled form of the learning mean-field control problem and the associate decoupled q-function (denoted by \(q_d\)), and establish its connection to the essential q-function to learn the optimal policy. In both formulations, we devise some model-free offline and online learning algorithms to take care of test policies stemming from the weak martingale conditions. In two concrete examples, one in LQ control framework and one beyond LQ control framework, we obtain the exact parametrization of the value function and all q-functions defined on the Wasserstein space and illustrate our algorithms with simulation experiments.

High-frequency anticipatory trading and its influences: small informed trader vs. front-runner

Ziyi XU Peking University: In this paper, the interactions between a large informed trader (IT, for short) and a high-frequency trader (HFT, for short) who can anticipate the former's incoming order are studied in an extended Kyle's (1985) model. Equilibria under various specific situations are discussed. Relying on the speed advantage, HFT always trades in the same direction as the large order in advance. However, whether or not she provides liquidity depends on her inventory aversion, the prediction accuracy, and the market activeness. She may supply liquidity back (act as a front-runner) or continue to take it away (in this case we call her a small IT). Small IT always harms the large trader while front-runner may benefit her. Besides, we find surprisingly that (1) increasing the noise in HFT's signal may in fact decrease IT's profit; (2) although providing liquidity, a front-runner may harm IT more than a small IT. This is a joint work with Xue CHENG (PKU).

Stock return forecasting based on heterogeneous graph neural network of industrial chain

Ke ZHOU Hunan University: This paper proposes a stock forecasting method based on a time-series heterogeneous graph attention network (GRU-HAN), which simulates the complex relationship between stocks by constructing a heterogeneous graph through the technical and economic connections among various industries. The proposed method consists of two parts: the Gated Recurrent Unit (GRU) and the Heterogeneous Graph Attention Network (HAN). For the first time, this paper uses a heterogeneous graph model to capture the relationship of the stock industry chain and conducts an empirical study on the Chinese A-share market. Existing research can be divided into two categories: single stock methods and group stock methods. The results of the study show that the proposed model exhibits good performance in terms of investment efficiency and ranking effect. The GRU captures the historical dynamic information of the stock and encodes the features of the price sequence, while the HAN models the relationship between the upstream and downstream heterogeneous graphs of the industrial chain. Existing deep learning-based stock prediction methods mainly focus on single stock prediction or homogeneous graph-based group stock prediction. However, they cannot establish heterogeneous graphs to simulate the comprehensive relationship between stocks.