Improved Algorithms for Computing Fisher's Market Clearing Prices

ACM Digital Library url: http://dl.acm.org/citation.cfm?id=1806731We give the first strongly polynomial time algorithm for computing an equilibrium for the linear utilities case of Fisher's market model. We consider a problem with a set B of buyers and a set G of divisible goods. Each buyer i starts with an initial integral allocation ei of money. The integral utility for buyer i of good j is Uij. We first develop a weakly polynomial time algorithm that runs in O(n4 log Umax + n3 emax) time, where n = |B| + |G|. We further modify the algorithm so that it runs in O(n4 log n) time. These algorithms improve upon the previous best running time of O(n8 log Umax + n7 log emax), due to Devanur et al.United States. Office of Naval Research (ONR grant N00014-05-1-0165

Auction algorithms for generalized nonlinear network flow problems

Thesis (Ph.D.)--Boston UniversityNetwork flow is an area of optimization theory concerned with optimization over networks with a range of applicability in fields such as computer networks, manufacturing, finance, scheduling and routing, telecommunications, and transportation. In both linear and nonlinear networks, a family of primal-dual algorithms based on "approximate" Complementary Slackness (ε-CS) is among the fastest in centralized and distributed environments. These include the auction algorithm for the linear assignment/transportation problems, ε-relaxation and Auction/Sequential Shortest Path (ASSP) for the min-cost flow and max-flow problems. Within this family, the auction algorithm is particularly fast, as it uses "second best" information, as compared to using the more generic ε-relaxation for linear assignment/transportation. Inspired by the success of auction algorithms, we extend them to two important classes of nonlinear network flow problems. We start with the nonlinear Resource Allocation Problem (RAP). This problem consists of optimally assigning N divisible resources to M competing missions/tasks each with its own utility function. This simple yet powerful framework has found applications in diverse fields such as finance, economics, logistics, sensor and wireless networks. RAP is an instance of generalized network (networks with arc gains) flow problem but it has significant special structure analogous to the assignment/transportation problem. We develop a class of auction algorithms for RAP: a finite-time auction algorithm for both synchronous and asynchronous environments followed by a combination of forward and reverse auction with ε-scaling to achieve pseudo polynomial complexity for any non-increasing generalized convex utilities including non-continuous and/ or non-differentiable functions. These techniques are then generalized to handle shipping costs on allocations. Lastly, we demonstrate how these techniques can be used for solving a dynamic RAP where nodes may appear or disappear over time. In later part of the thesis, we consider the convex nonlinear min-cost flow problem. Although E-relaxation and ASSP are among the fastest available techniques here, we illustrate how nonlinear costs, as opposed to linear, introduce a significant bottleneck on the progress that these algorithms make per iteration. We then extend the core idea of the auction algorithm, use of second best to make aggressive steps, to overcome this bottleneck and hence develop a faster version of ε-relaxation. This new algorithm shares the same theoretical complexity as the original but outperforms it in our numerical experiments based on random test problem suites

The Virtues and Vices of Equilibrium and the Future of Financial Economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.Equilibrium, Rational expectations, Efficiency, Arbitrage, Bounded rationality, Power laws, Disequilibrium, Zero intelligence, Market ecology, Agent based modeling

Applying Blockchain Technology to Financial Market’s Infrastructure

The utilization of blockchain technology has gained widespread acceptance across various domains in recent years. Among them, blockchain integration in the financial sector is particularly noteworthy. Blockchain technology offers a range of features that can address various challenges in the financial industry, including decentralization, transparency, enhanced security, and tamper-proofing. Therefore, this thesis aims to investigate the issues that persist in academia and industry and address them through blockchain technology. The research for this thesis was divided into three major stages. The first stage involved conducting an academic survey through a comprehensive literature review. The aim was to identify the pain points that academics have identified and to narrow down the problems that concern the academic community. The second stage involved collecting requirements from industry experts. This helped to identify the real-world issues that currently exist in the financial industry. Based on these issues, the research moved on to the next stage. The third stage involved an experimental study, further divided into two parts. Part 1 involved designing and developing a blockchain-based issuance and trading system for financial products. This system aimed to enhance participant trust, reduce costs, and increase efficiency. Part 2 involved the development of a risk monitoring system for blockchain-based financial products. This system aimed to assist participants in monitoring market risks, providing them with risk warning coefficients, and reducing the probability of systemic risks in the market. The results of this thesis demonstrate that blockchain technology's feasibility and integration can positively impact financial markets from an experimental perspective. It can be helpful to adopt blockchain technology for financial and FinTech industries