NCKH Giảng viên

Abstract: We provide a strategic model of the formation of production networks that subsumes the standard general equilibrium approach. The objective of firms in our setting is to choose their supply relationships so as to maximize their profit at the general equilibrium that unfolds. We show that this objective is equivalent to the maximization by the firms of their eigenvector centrality in the production network. As is common in network formation games based on centrality, there are multiple Nash equilibria in our setting. We have investigated the characteristics and the social efficiency of these equilibria in a stylized version of our model representing international trade networks. We show that the impact of network structure on social welfare is firstly determined by a trade-off between costs of increasing process complexity and positive spillovers on productivity induced by the diversification of the input mix. We further analyze a variant of our model that accounts for the risks of disruption of supply relationships. In this setting, we characterize how social welfare depends on the structure of the production network, the spatial distribution of risks, and the process of shock aggregation in supply chains. We finally show that simple trade policies characterized by sets of links that are either prevented or catalyzed can be a powerful equilibrium selection device.

In this presentation, using renewal times and Girsanov’s transform, we prove that the speed of the excited random walk is infinitely differentiable with respect to the bias parameter in (0,1) in dimension d≥2. At the critical point 0, using a special method, we also prove that the speed is differentiable and the derivative is positive for every dimension 2≤d≠3. However, this is not enough to imply that the speed is increasing in a neighborhood of 0. It still remains to prove that the derivative is continuous at 0.
We also introduce a method for studying monotonicity of the speed of excited random walks in high dimensions, based on a formula for the speed obtained via cut-times and Girsanov’s transform. While the method gives rise to similar results as have been or can be obtained via the expansion method of van der Hofstad and Holmes, it may be more palatable to a general probabilistic audience.

Efficiency and fairness stand as primary goals in designing economic systems, offering benchmarks for evaluating economic solutions. Nevertheless, achieving perfectly efficient and fair utopian economies proves unfeasible due to factors like incentives, lack of information, computational hardness, etc. In this talk, we confront this inherent impossibility using methodologies derived from the realm of approximation algorithms. We illustrate techniques for establishing and refining designs that offer provably guaranteed approximations on an ideal yet impossible level of efficiency and fairness. Along the way, we delve into several unresolved questions that have captured the attention of researchers in the field.

Abstract: In economic analysis, decision makers often face the necessity of making trade-offs between costs and benefits occurring at various points in time, including those related to environmental concerns. The predominant discounting approach frequently employed is characterized by an exponential form. Central to this approach is the discount rate, a unique parameter that converts a future value into its present equivalent. However, it is noteworthy that a universally accepted discount rate for the assessment of such decisions remains a matter of ongoing debate and lacks consensus. This paper presents a novel approach that provides a robust solution for resolving conflicts in discount rates. This approach recommends considering all discount rates but aims to assign varying degrees of importance to these rates in the decision-making process. Moreover, a considerable number of economists support a theory that suggests equal consideration of future and present benefits. In response to this debate, we introduce a general criterion capable of accommodating situations where it is feasible not to discount future utilities. This criterion encompasses and extends various existing criteria in the literature.

Trong bài nói chuyện này, tôi sẽ giải thích tại sao Tối ưu hóa được coi là một người hùng thầm lặng của Trí tuệ nhân tạo. Tôi cũng đưa ra các luận điểm khuyến nghị các trường đại học nói chung và các khoa Toán ứng dụng nói riêng cần đầu tư nhiều hơn nữa vào Tối ưu hóa. Để minh họa cho tầm quan trọng và sự thú vị của Tối ưu hóa, tôi sẽ trình bày một nghiên cứu mới được công bố gần đây và một dự án nghiên cứu ứng dụng làm sản phẩm cho doanh nghiệp mà nhóm chúng tôi đã thực hiện tại Việt Nam.

 Abstract: A monopolistic seller jointly designs allocation rules and (new) information about a pay-off relevant state to a buyer with private types. When the new information flips the ranking of willingness to pay across types, a screening menu of prices and threshold disclosures is revenue maximizing. Conversely, when its impact is marginal, bunching via a single posted price and threshold disclosure is (approximately) optimal. While information design expands the scope for random mechanisms to outperform their deterministic counterparts, its presence leads to an equivalence result regarding sequential versus static screening.

Abstract: In this talk, we would like to briefly review some real-life applications of Machine Learning for E-commerce platforms. Next, we will discuss in detail our recent approaches and results for Product Identification Problem in E-commerce

Abstract: Customer Segmentation is one of the most important topics in the marketing field. Traditional customer segmentation methods such as RFM (Recency, Frequency, and Monetary) and its variants have a major drawback of segmenting customers based only on some dimensions of customer behavior. Our research proposes a novel approach to overcome this issue. In the first step, we create the maximum possible features from the transactional dataset that can simulate customer consumption behavior. In the second step, we use GMM(Gaussian Mixture Model) combined with the feature selection method to segment our customer base. We also compare the traditional approach with a novel method using some business metrics. We show that 91% of customers in the golden group found by the novel approach making at least one transaction for six continuously consecutive months in the future, 84% of them is in the top 10% of highest monetary value customer in 2011. These number is only 76% and 74%, corresponding to the traditional method.

Abstract: In this work, we study a stochastic spatial epidemic model where the N individuals are characterized by their position and infection state. We begin with a microscopic description in which the displacement of individuals is driven by mean-field interactions, a state-dependent diffusion, and a common environmental noise. The evolution of epidemiological states is described by Poisson point processes with an infection rate depending on the distribution of other nearby individuals, also of the mean-field type. Then, we study the behavior of this system at the macroscopic level when the population size is large.

Abstract: Định lý thứ nhất của phúc lợi kinh tế trong mô hình kinh tế cổ điển là phân bổ nguồn lực ở trạng thái cân bằng sẽ là hiệu quả. Tuy nhiên, điều này không đúng khi hành vi của người tiêu dùng bị ảnh hưởng bởi các yếu tố ngoại lai. Trong nghiên cứu này, chúng tôi chứng minh là có thể dùng thuế VAT và các khoản trợ cấp để cải thiện tính hiệu quả của điểm cân bằng trong mô hình có yếu tố ngoại lai.

ChatGPT là công nghệ AI được lan truyền rộng rãi với khả năng đáng kinh ngạc trong việc trả lời các câu hỏi trong nhiều lĩnh vực khác nhau, cũng như giao tiếp rất tự nhiên với con người trong cuộc đối thoại. Tuy nhiên nền tảng công vệ về xử lý ngôn ngữ tự nhiên, học tăng cường đằng sau ChatGPT ít được đề cập tới. Thế nên trong seminar này, tôi sẽ trình bày về các kĩ thuật để ra được mô hình ChatGPT. Thêm vào đó, tôi sẽ thảo luận về các ứng dụng thiết thực của ChatGPT, cũng như những giới hạn hiện tại của mô hình này.

The co-existence of external referencing pricing (ERP) and reimbursement policy is common in many countries. Thus, this research examines whether or not the imposition of ERP is socially desirable in the presence of the reimbursement policy. For the direct sales channel, we find that the home social welfare is worse off with ERP if the home copayment rate is too high. Our main results are robust under indirect sales channels. Moreover, the home social welfare under the pharmacy purchasing-price (PPP) ERP is larger than that under the ex-factory-price (EFP) ERP if the home copayment rate is high enough. Finally, the profit of the brand-name firm under indirect sales channels is higher than that under direct sales channels if the home copayment rate is too high.

Portfolio optimization is one of the most basic skills you’ll need to acquire when actively managing your investments. In this work, the problem of choosing a portfolio that maximizes a certain utility function of asset returns is presented from the academic work to the financial industry. The utility function is a convex function of the portfolio weights, and the portfolio optimization problem can be formulated as a convex optimization problem. Then, we introduce a well-known and effective toolbox to solve this problem in the financial industry.

This talk discusses Graph Analysis and its applications in the banking industry. Graph Analysis provides a powerful tool for data analysis to understand complex relationships and patterns in the data, allowing us to make more informed decisions and improve overall performance. This talk is threefold, and we will first summarize some key notations of graphs. Secondly, we review some important algorithms in graph theory and applications. Finally, we explore real applications of the graph in the bank area.

Many random quantities in finance can be modeled as solutions of stochastic differential equations. Some well-known models are the Black-Schole model for stock prices, the Cox-Ingersoll-Ross model for spot interest rates… In many applications, stochastic differential equations do not have a closed-form solution. Therefore, it can only be solved by numerical methods. This talk presents some recent numerical approximation methods for stochastic differential equations with irregular coefficients.

We consider a continuous Gaussian random field living on a compact set T. We are interested in designing an asymptotically efficient estimator of the probability that the integral of the exponential of the Gaussian process over T exceeds a large threshold u. We propose an Asmussen–Kroese conditional Monte Carlo type estimator and discuss its asymptotic properties according to the assumptions on the first and second moments of the Gaussian random field. We also provide a simulation study to illustrate its effectiveness and compare its performance with the importance sampling type estimator of Liu and Xu (2014a)