Blockchain Papers

Matteo Bonforte, Maria Gualdani, Peio Ibarrondo

No abstract is available for this record.

Min Li, Na Li, Na Li, Zhen Wu

This paper is concerned with a class of linear-quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by individual noise, and all agents are coupled together via the control average term. Using the mean-field game approach and the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward-backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. By the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related $\varepsilon$-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

Leibing Xiao, Xinchao Wei, Yuelei Xu, Xin Xu · 7 authors

This paper investigates portfolio management algorithm for the cryptocurrency market by using the TQC (Truncated Quantile Critics) algorithm. The study is based on the daily prices of cryptocurrencies. TQC is a deep reinforcement learning algorithm with the Actor-Critic architecture. It alleviates the overestimation problem of traditional value learning algorithm. In this paper, the data of cryptocurrencies are first processed as input to the networks. The inputs to the networks include not only the closing prices of cryptocurrencies, but also the relative strength index, moving average line, and moving average convergence divergence. Various metrics measuring algorithm returns and algorithm stability are used as evaluation criteria in this paper. In this paper, common deep reinforcement learning algorithms are compared. The experimental results show that the TQC algorithm has a highest return of 33.9 % during the test period, which is 3 %, 3 % and 15.6 % higher than A2C, PPO and DDPG respectively. And, the TQC algorithm has the highest stability of return, which is an important evaluation metric for portfolio management algorithms. Despite the high volatility of the cryptocurrency market, the performance of the TQC algorithm has remained relatively stable. This illustrates the positive effects of the TOC algorithm.

Zhenghong Qiu, Jianhui Huang, Tinghan Xie

This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be indefinite in cost functional. This setup is innovative and has great theoretical and realistic significance as its applications in mathematical finance (e.g., portfolio selection in mean-variation model). Using some fully-coupled variational analysis under the person-by-person optimality principle, and the mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with embedding representation. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.

Mattia Bongini, Massimo Fornasier

In recent years, numerous studies have focused on the mathematical modeling of social dynamics, with self-organization, i.e., the autonomous pattern formation, as the main driving concept. Usually, first or second order models are employed to reproduce, at least qualitatively, certain global patterns (such as bird flocking, milling schools of fish or queue formations in pedestrian flows, just to mention a few). It is, however, common experience that self-organization does not always spontaneously occur in a society. In this review chapter we aim to describe the limitations of decentralized controls in restoring certain desired configurations and to address the question of whether it is possible to externally and parsimoniously influence the dynamics to reach a given outcome. More specifically, we address the issue of finding the sparsest control strategy for finite agent-based models in order to lead the dynamics optimally towards a desired pattern.

Mattia Bongini, Massimo Fornasier, ,Technische Universität München, Facultät Mathematik, Boltzmannstrasse 3, D-85748, Garching bei München

Conditional self-organization and pattern-formation are relevant phenomena arising in biological, social, and economical contexts, and received a growing attention in recent years in mathematical modeling. An important issue related to <em> optimal government strategies</em> is how to design external parsimonious interventions, aiming at enforcing systems to converge to specific patterns. This is in contrast to other models where the players of the systems are allowed to interact <em> freely</em> and are supposed autonomously, either by game rules or by embedded decentralized feedback control rules, to converge to patterns. In this paper we tackle the problem of designing optimal centralized feedback controls for systems of moving particles, subject to mutual attraction and repulsion forces, and friction. Under certain conditions on the attraction and repulsion forces, if the total energy of the system, composed of the sum of its kinetic and potential parts, is below a certain critical threshold, then such systems are known to converge autonomously to the stable configuration of keeping confined and collision avoiding in space, uniformly in time. If the energy is above such a critical level, then the space coherence can be lost. We show that in the latter situation of lost self-organization, one can nevertheless steer the system to return to stable energy levels by feedback controls defined as the minimizers of a certain functional with $l_1$-norm penalty and constraints. Additionally we show that the optimal strategy in this class of controls is necessarily <em> sparse</em>, i.e., the control acts on at most one agent at each time. This is another remarkable example of how <em> homophilious</em> systems, i.e., systems where agents tend to be strongly more influenced by near agents than far ones, are naturally prone to sparse stabilization, explaining the effectiveness of parsimonious interventions of governments in societies.

Ken‐ichiro Ogawa, Yoshihiro Miyake

Abstract The reaction‐diffusion model is one of the theoretical approaches used to realize autonomous decentralized systems. The model conventionally assumes that all components of a system locally interact with each other under ideal conditions, ignoring any effect from the environment. However, it has recently become clear that nonlocal interactions mediated by the environment play an important role in the ontogenesis of multicellular organisms, a typical autonomous decentralized system. In this paper, we discuss the “redifferentiation” phenomenon of cancer cells in which such a nonlocal interaction is considered to play an essential role. Further, we propose a model to reproduce this phenomenon and mathematically analyze our model to construct autonomous decentralized systems with nonlocal interactions mediated by the environment in the future. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(7): 55–65, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ ecjc.10101

美博 三宅, Yoshihiro Miyake

No abstract is available for this record.