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This study presents a comprehensive empirical analysis integrating Harry Markowitz Mean–Variance Optimization, Monte Carlo simulation, utility-based portfolio selection, and Random Forest machine learning within the context of the Mongolian Stock Exchange (MSE). Using 32 months of monthly closing price data from September 2023 to April 2026 for 12 actively traded equities and the TOP-20 index, the study constructs and compares three traditional portfolios—Equal Weight, Minimum Variance, and Maximum Sharpe—together with a machine-learning-augmented portfolio. The findings provide three main contributions. First, the empirical results demonstrate that Markowitz optimization can significantly outperform passive index investment on the MSE in terms of risk-adjusted performance. Second, the study offers practical capital allocation guidance based on the Capital Allocation Line (CAL) for investors with different levels of risk aversion. Third, the Random Forest-augmented portfolio shows potential to improve both return and Sharpe performance relative to traditional approaches, although longer time-series data are necessary to fully realize the advantages of machine learning in portfolio optimization. Future research may extend this framework by incorporating LSTM and Gradient Boosting algorithms, macroeconomic variables, and portfolio weight constraints (w_iⓜ≤25%)to mitigate concentration risk and improve portfolio stability.
Abstract. In a network, nodes are considered critical if their removal significantly disrupts connectivity. Identifying these nodes is essential for understanding structural vulnerabilities in systems ranging from telecommunications and social networks to military strategy and epidemiological modeling. However, in many practical scenarios, connectivity is only vital between a specific subset of nodes, known as terminals. This paper investigates the Terminal-Aware Critical Node Detection problem. We examine two variants: one where terminals may be deleted and another where they are protected. Our objective is to minimize the pairwise connectivity among terminals in the residual graph by removing at most k nodes. We present two Mixed-Integer Programming (MIP) formulations alongside several heuristic methods. Computational experiments on random graphs with varying size, density, terminal count, and budget demonstrate that our heuristics provide high-quality solutions efficiently compared to exact methods.
ABSTRACT New ideas and initiatives not only drive technological transformation but also bring about profound changes in global industrial structures, economic systems, and the social environment of humanity. The ongoing Fourth Industrial Revolution—currently serving as a primary accelerator of contemporary economic development—has shifted the organization of production toward centralized programmable control while enabling next-generation applications in robotics, artificial intelligence, big data, 3D printing, nanotechnology, and biotechnology. Characterized by rapid diffusion, broad scope, and simultaneous impact across all levels of socio-economic systems, this transformation compels nations to promptly align their policies, education systems, and innovation environments with the emerging technological paradigm. This study aims to systematically analyze and determine the influence of the entrepreneurial ecosystem on the development of start-ups in Mongolia. The results reveal that human capital and the government policy environment exert the strongest effects within the start-up ecosystem. These findings correspond to two observed patterns: (i) most Mongolian start-ups originate within university-affiliated structures, and (ii) participation from the industry sector—considered a core stakeholder in mature entrepreneurial ecosystems—remains notably weak or almost absent. Accordingly, the study concludes that fostering multi-stakeholder collaboration, particularly through strong and proactive public–private partnerships supported by targeted government policies, is essential for the sustainable development of start-ups in Mongolia. Multiple linear regression analysis was employed as the primary methodological approach. Keywords: Innovation, start-up ecosystem, regression analysis
Critical node detection involves identifying key nodes whose removal significantly disrupts network connectivity or performance. The evaluation of vulnerability in networks is crucial because many real-world problems are represented as graphs with uncertainty, including social networks, communication infrastructures, epidemiological models, and transportation systems. In this paper, we consider a stochastic Critical Node Detection Problem (SCNDP) with edge uncertainty, aiming to minimize the expected pairwise connectivity (EPC) in the resulting residual network. We propose a heuristic method for the SCNDP and compare it with the existing algorithm. Experimental results performed on random graphs with different edge-probability configurations demonstrate the effectiveness of the heuristics.
In this study, we formulate a bilevel critical node detection problem for a given threat level and a budget. A leader has a budget to immunize a subset of nodes. An attacker, with the knowledge of the leader’s choice, will remove any set of non-immunized nodes within their budget, which is the threat level. The leader seeks to maximise the pairwise connectivity of the nodes for the worst case removal strategy of the attacker. We solve this problem using a high point relaxation within a branch-and-bound framework. We introduce some valid inequalities to strengthen the formulation and introduce a branching strategy to deal with the bilevel infeasibility. We test this procedure on two graph families with varying number of nodes, edge densities and budgets and share our computational experience.
In this chapter, we survey the work on four problems each involved in identifying critical nodes in a network from very different perspectives. We provide them as generalizations of classical graph problems but they can also be directly motivated from an application point of view. We formally introduce all four problems and briefly look at their characterizations. We also look into a few computational methods that were used in the literature to solve them. We conclude with some future lines of investigation on all these problems.
Abstract. The Global Fund Allocation problem (GFAP) is a variation of bilevel knapsack problem which comprises of two players, a leader and a follower each equipped with a budget. There is a set of projects that have certain costs. In the setting we consider, the profit valuations of these projects is the same for both leader and the follower and projects can be fractionally picked. In addition, there is a special project of exclusive interest to the follower (i.e. leader’s profit for this project is 0). The leader is interested in providing a cost offset to these projects such that the total offset is within the leader’s budget. The follower then solves a paramterised continuous knapsack problem that considers the projects with the offsetted cost. The leader’s objective is to maximise the profits of the projects selected. In this work, we provide a complexity result and a polynomial time approximation scheme for this special case of the GFAP. This bilevel problem has continuous variables at both the upper level and lower level but the bilevel nature makes this a difficult problem to solve.
In this talk, we present three different approaches to solve a cascading model of node activations or an information propagation model in a network. The nodes are in two different states and the state of an ”inactive” node turns “active” depending on the states of its neighbors. The combined states of the nodes of the graph determines the state of the network, which is directly related to the operational efficiency of the network. Mixed integer programming formulations are presented and solution approaches to the problems are proposed. Moreover, leveraging the advances in graph representation learning, we provide deep reinforcement learning model for the problem. We find a reinforcement learning model provides competitive heuristics with faster runtime and better scalability.
In this paper, we provide three different approaches to solve a cascading model of node activations or an information propagation model in a network. The nodes are in two different states and the state of an ”inactive” node turns “active” depending on the states of its neighbors. The combined states of the nodes of the graph determines the state of the network, which is directly related to the operational efficiency of the network. Mixed integer programming formulations are presented and solution approaches to the problems are proposed. We also present a heuristic algorithm and a reinforcement learning algorithm to the problems.
The topic of machine learning and artificial intelligence has recently attracted a lot of attention. In particular, as the use of technology increases, so does the amount of data available for machine learning, resulting in advances in technology such as facial recognition and image processing. However, the use of machine learning methods is not limited to the technology sector and can also be applied to the economic and financial sectors. In this study, we use factors analysis and unsupervised machine learning methods, namely hierarchical cluster method and k-means method, to make clusters of economies using the indicators related to countries' economic policy and debt. We extracted the data of 217 countries’ 345 indicators, grouped as economic policy and debt indicators out of 1,440 indicators that are considered World Development Indicators by the World bank, and used the last 15 years of data to make 4 clusters of countries. Clustering countries by their economic characteristic or by their indicators, using machine learning methods can help identify countries that have similar economic characteristics and will be useful in analyzing the differences between clusters. Keywords: hierarchical clustering, factor analysis, Economic Policy and Debt Indicators, python
Today, artificial intelligence and machine learning play increasingly important roles in financial decisions due to quantitative nature of the sector. We have seen successful applications of machine learning in many areas of finance including portfolio optimization, fraud detection, risk management and credit underwriting. In this paper, we use one of the most popular machine learning techniques, K-means, to analyze listed companies on the Mongolian Stock Exchange based on similarity measures of their financial indicators. Financial statement data of 2019 on 128 companies are used and 7 financial ratios are selected as features. Then, k-means clustering technique is applied to the data and, as a result, the companies are clustered into 8 different clusters for each year. We explain how k-mean clustering can be used for credit analysis and portfolio selection. Our clustering is also compared with the current ranking system of the Mongolian Stock Exchange.
Motivated by the fact that pay-per-use rentals require firms to be responsible for the the operational costs of products and service support network, we establish a pay-per-use rental model where a firm strategically sets the availability of products for rentals to achieve the trade-off between production quantity and operational costs. Furthermore, based on the traditional sale model, we also propose a combined model of sale and pay-per-use rental. The objective is to maximize firm’s profits under three models: the sale model, the pay-per-use rental model, and the hybrid model of sale and rental. The approach of backward induction is adopted to obtain the firm’s optimal decisions on pricing and production volume. Through comparative analysis, we provide the firm’s global optimal strategic solution, and the corresponding solutions in different market environments are developed, respectively, due to the variance of polling effects and costs. The results show that under the no-pooling case where customers’ requests overlap completely, the hybrid model always show higher profitability than the pay-per-use rental model, and it performs better than the sales model only when the per-unit operational and production costs are low. Under the perfect-pooling case where customers’ requests do not overlap, the hybrid model is always the optimal strategy. Numerical experiments are also conducted to illustrate the results under the general pooling case.
Motivated by the fact that pay-per-use rentals require firms to be responsible for the the operational costs of products and service support network, we establish a pay-per-use rental model where a firm strategically sets the availability of products for rentals to achieve the trade-off between production quantity and operational costs. Furthermore, based on the traditional sale model, we also propose a combined model of sale and pay-per-use rental. The objective is to maximize firm’s profits under three models: the sale model, the pay-per-use rental model, and the hybrid model of sale and rental.
