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Dynamic Optimization of Consumption and Foreign Debt, and Renewable Resource Export in MSY Policy
Get PDFThe present paper studies the problems of dynamic optimization of consumption and foreign debt, and (natural) renewable resource export in the MSY policy of a small (developing ) country. Its fundamental model is formulated by utilizing a dynamic macro-economic model based on the two differential equations of Rauscher [1989] with an extension introducing an ecological management policy, namely the maximum sustainable yield (MSY) policy, and some other alterations.
The basic dynamic system of Rauscher [1989] is the two differential equation system with regard to the population growth of a (natural) renewable resource to be exploited and exported by a firm, and the accumulation of foreign debt through the international trade of exported resources and imported goods (of consumption and users’ costs) by a small (developing) country.
The introduction of the MSY policy into the model makes the dynamic system of its fundamental model so simple mathematically that the two equation basic dynamic system is simplified to one differential equation as its basic dynamic system. This means that its main dynamic system consists of one state variable, foreign debt stock (that is the accumulation of foreign debt), and one control variable, consumption flow. The other state variable is controlled directly by the MSY policy.
The main results are two theorems based upon three lemmas earned by the dynamic optimizing study of the fundamental dynamic system which consists of (1), (2), (3), (4), (6), and (7) with concerning assumptions and functions. Theorem 1 is nominally simpler than the result of Rauscher [1989] and asserts that, supposing the levels of two important parameters are moderate values, the long-run equilibrium of the system becomes a saddle point and a unique path to approach monotonically from the initial condition and reach the only equilibrium point. Such a unique path is the optimal time path or the optimal trajectory while maintaining the MSY policy for the small country.
Theorem 2 asserts that there are some comparative static effects of the important parameters upon the only long-run equilibrium of the system. Its foreign debt stock is not affected by the levels of resource price and profit rate, and the MSY at all, but is affected positively only by the utility discount rate over time. And then its consumption level is affected positively by the levels of resource price and profit rate, the effect of the level of the MSY is positive or zero, but is affected negatively only by the utility discount rate over time.departmental bulletin pape
Determinants of Beijing residents' behavior in purchasing environmentally friendly rice
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Some Properties of Generalized Homothetic Robust Epstein-Zin Utility
Get PDFIn the context of Knightian uncertainty, homothetic robust Epstein-Zin (HREZ) utility is a promising one among robust utilities. Thispaper investigates some properties of “generalized homothetic robustEpstein-Zin (GHREZ) utility,” in which the coefficient of relative ambiguityaversion in HREZ utility is generalized to the matrix of relativeambiguity aversions. The study demonstrates that GHREZ utility is“generalized stochastic differential utility (SDU)”, while HREZ utilityis SDU. The paper then presents properties of ambiguity aversions ofGHREZ utility. The study introduces concepts of directional ambiguityaversions, and demonstrates properties of directional ambiguityaversions of GHREZ utility.technical repor
フクザツ ナ コウゾウ オ モツ コウジゲン データ ノ ヘンスウ スクリーニング ホウ ニ カンスル ケンキュウ
Get PDF滋賀大学博士（データサイエンス）Regression analysis is widely used to model relationships between variables and is applied in applications such as future prediction and measuring the effect of variables. For example, to understand the regularity of product sales, sales are treated as the response variable, while product attributes (for example, price, color, size, etc.) serve as predictors. The predictive accuracy and interpretability of the model are considerably affected by the variables included in the model. Appropriate variable selection enhances model accuracy and interpretability, resulting in improved decision-making and outcomes across various fields.
Several methods have been devised for variable selection. The stepwise method sequentially adds or removes variables to improve the model, whereas regularization methods with sparsity-inducing penalties reduce some coefficients to zero by applying a penalty based on the size of regression coefficients. However, for high-dimensional data, where the number of variables considerably exceeds the sample size, the computational cost becomes substantial because of the large number of variables and tuning parameters requiring evaluation. Moreover, these methods often fail to consistently identify the truly important variables.
Numerous screening methods have been proposed to address these problems. These methods evaluate the correlation between each predictor and the response, selecting variables with strong correlations. By evaluating predictors individually, screening methods are computationally efficient. Additionally, many screening methods exhibit the sure screening property, which ensures that the probability that the selected variables contain truly important variables converges to one as the sample size increases. However, their performance degrades in the presence of multicollinearity, and they typically do not account for interactions among predictors. Real data often exhibit complex structures, such as multicollinearity and interactions, which, if not addressed, can reduce model accuracy and interpretability.
This thesis proposes novel approaches to handle multicollinearity and interactions, respectively. First, we introduce a screening method that improves variable selection in the presence of multicollinearity by modifying an existing factor analysis-based approach. The existing method uses factor analysis on predictors to transform the data and reduce multicollinearity. However, it can unintentionally discard too much information about important predictors, leading to lower variable selection performance. The proposed method prevents this problem by truncating a portion of specific common factors obtained by factor analysis during the transformation process, with the truncation determined objectively using a BIC-type criterion. After appropriately transforming to remove multicollinearity, we select predictors that have large absolute values of correlation with the response. A theoretical model based on the eigenvalue distribution demonstrates the improved performance of the proposed method. Simulated and real data analyses confirm its effectiveness.
Second, we propose an interaction screening method that enhances variable selection performance for multi-class classification problems by modifying an existing approach based on Kendall’s rank correlation coefficient. The proposed method focused on an approach that does not consider assumptions about the existence of main effects and directly determines the importance of the interactions because, in some cases, only interactions are meaningful in the real world. The existing method directly computing the importance of interactions tends to underestimate the importance of interactions related to minor classes in datasets with highly imbalanced class labels because its importance score depends on correlations calculated from all of the sample and on the ratios of class sample sizes. To address this issue, the proposed method incorporates correlations computed using data from each class and the average ratios of sample sizes across multiple classes. The proposed interaction importance scores more accurately reflect the information from the minor classes. Additionally, we show that the proposed method satisfies certain theoretical properties. One is the sure screening property. Another is the ranking consistency property, which guarantees that interactions truly related to the response obtain higher importance scores than unrelated interactions. Using the ranking consistency property, we can identify the truly important set of interactions by selecting interactions in order of their importance scores if the number of important interactions is known and the sample size is sufficiently large. Simulated and real data analyses reveal that the method effectively identifies important interactions even in imbalanced datasets.doctoral thesi
