Asymptotic Portfolio Strategy Based on the CEV Model with General Utility Function

The optimal investment problem is a hot field of financial risk control. The analytical solution of investment strategy can be obtained with the power function utility and exponential function utility when the stock price obeys the constant elasticity of variance (CEV) model. However, different investors have different risk preferences; it means that different investors have different utility functions. In this paper, we propose an asymptotic analysis method to obtain the asymptotic solution of investment strategy with the general utility function. The value function is expanded in the form of series, the expressions of the zero-order term and first-order term of the series expansion are derived, respectively, and the error between the asymptotic approximation and the optimal value function is calculated. Finally, the numerical examples provide comparative analysis between the analytical solution and the asymptotic solution to verify the effectiveness of the proposed method.

Public Input Provision, Tax Base Mobility, and External Ownership

This article investigates the distortionary impacts of tax base mobility and external ownership on public input provision. Regional governments compete for mobile tax bases (e.g., business capital). The impact of regional public policy partially accrues to non-residents because immobile factors (e.g., business land) are subject to external ownership. This article derives an optimal rule for regional public input provision that illustrates how these two distortionary impacts depend on the nature of production functions. The impact of external ownership is particularly complex. To explore this impact in detail, the case of production functions with constant elasticity of substitution is examined. Public inputs with different productivity impacts yield fairly different implications of external ownership for inefficient public input provision.

An Investor’s Investment Plan with Stochastic Interest Rate under the CEV Model and the Ornstein-Uhlenbeck Process

The aim of this paper is to maximize an investor’s terminal wealth which exhibits constant relative risk aversion (CRRA). Considering the fluctuating nature of the stock market price, it is imperative for investors to study and develop an effective investment plan that considers the volatility of the stock market price and the fluctuation in interest rate. To achieve this, the optimal investment plan for an investor with logarithm utility under constant elasticity of variance (CEV) model in the presence of stochastic interest rate is considered. Also, a portfolio with one risk free asset and two risky assets is considered where the risk free interest rate follows the Ornstein-Uhlenbeck (O-U) process and the two risky assets follow the CEV process. Using the Legendre transformation and dual theory with asymptotic expansion technique, closed form solutions of the optimal investment plans are obtained. Furthermore, the impacts of some sensitive parameters on the optimal investment plans are analyzed numerically. We observed that the optimal investment plan for the three assets give a fluctuation effect, showing that the investor’s behaviour in his investment pattern changes at different time intervals due to some information available in the financial market such as the fluctuations in the risk free interest rate occasioned by the O-U process, appreciation rates of the risky assets prices and the volatility of the stock market price due to changes in the elasticity parameters. Also, the optimal investment plans for the risky assets are directly proportional to the elasticity parameters and inversely proportional to the risk free interest rate and does not depend on the risk averse coefficient.

Implementation of Constant Elasticity of Substitution Function and Data Envelopment Analysis: Productivity and Technical Efficiency of Large Industry Creative Economy in Craft Subsector Indonesia

Indonesia has undergone a transformation from agriculture to the manufacturing industry in 1971-1997. In the 2001-2015 period there was de-industrialization in developed countries. Likewise, Indonesia which shows a decrease in the contribution of GDP and manufacturing sector workforce to the economy. However, deindustrialization in Indonesia is premature / too fast. One of the policies to overcome this problem is with attention to the creative industry. With the existence of the creative industry, it can achieve several SDGs goals, namely the 8th goal, namely decent work and economic growth, the creative economy can increase economic growth, create jobs and increase exports (UNCTAD, 2010). However, the creative industry GDP growth that is below the RPJMN target is thought to indicate low productivity of the creative industry. According to IBS data, the craft sub-sector creative industry has a low production value. To see productivity can use technical efficiency. This study aims to evaluate the technical efficiency of creative industry in the craft sub-sector as well as to analyze the trend of variables that affect technical judgments. The method used is the CES production function and Data Envelopment Analysis. The results show that industries that have high total production factor values have a tendency to have high technical efficiency values as well. Furthermore, those arranged according to technical categories and binary logistic regression are used to determine trend variables that affect technical judgments. The technical efficiency of the craft, significantly by wages, investment status and company scale.

Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

Modeling the Dynamics of Gross Regional Product

The gross regional product is a key macroeconomic indicator that characterizes the development of the regional socio-economic system. Modeling the dynamics of this indicator, as the final product of the economic system, also involves the development of models for changing the values of aggregated cost factors associated with its production. One of the directions of using the developed models is the formation of short-term forecasts of the direct values of the gross regional product and the factors of labor and capital costs of the regional economy that determine them. Aim. Modeling the dynamics of the value of the gross product of the regional economy of the Yamal-Nenets Autonomous Okrug on the basis of the one-sector model of R. Solow for the formation of short-term forecasts of the value of this indicator. Materials and methods. The one-sector model of economic growth by R. Solow is used, in which the functioning of the regional economy is described by two-factor neoclassical functions with a constant elasticity of substitution of factors of production costs. Production functions are identified using retrospective sequences of indices of gross regional product and cost factors of the regional economy. Short-term forecasting of the gross product of the regional economy is carried out using a production function that provides a better approximation of retrospective data of the time interval of the previous forecasting year. Results. Neoclassical two-factor production functions with constant elasticity of substitution of cost factors of the regional economy of the Yamalo-Nenets Autonomous Okrug (YNAO) for the period from 2001 to 2018 were constructed.The values of the gross regional product and the average annual number of employed in the Yamal-Nenets economy were calculated for 2017–2019, which were compared with the corresponding data published by the Federal State Statistics Service of the Russian Federation, and the forecast values published by the regional administration. Conclusion. It has been established that the used production functions give acceptable estimates of the approximation of the actual values of the gross regional product of the considered regional economy in the considered time interval. Modification of the models for changing the values of cost factors made it possible to increase the accuracy of short-term forecasts, both directly of the values of the gross regional product and the values of factors of labor and capital costs.

Dynamic Compression Model Incorporating Elastic Nonlinearity of Paperboard

Spring of constant elasticity is a concept from theories of extension while elastic nonlinearity in compressive deformation is a general phenomenon for polymeric materials involved in offset or flexographic printing, paper board, polymer plate, and cushioning tape. This phenomenon needs therefore to be coped with by the model of printing dynamics. We hereby present an extended approach based on the Maxwell material model. In the extended approach, a compression process is subdivided into (or approximated by) sequential subprocesses. The elastic modulus may vary from one subsection to another but remains constant in each of the subprocesses. With the extended approach dynamic behaviours (compression/recovering) of paperboard can be reproduced and predicted. As a concrete example, dynamic behaviours of paper board in the print nip were simulated with satisfactory outcome. The simulation also revealed that viscoelasticity of the board is the origin of mechanical hysteresis of the stress–strain curve. Due to viscoelasticity and nonlinearity of the materials careful design is essential to simulate full-scale printing with a lab press.

Income and factor substitution: an investigation on the Solow growth model under the constant elasticity of substitution

PurposeThe purpose of this study is to examine whether the elasticity of substitution (ES) varies between developed and developing countries.Design/methodology/approachThe author derives the growth regressions from the Solow model under the constant elasticity of substitution production function by using the first-order Taylor series expansion and estimate them for each country group classified based on time-varying behavior of income per worker using the data-driven algorithm.FindingsThe ES is not unitary and varies among country groups. Developed countries generally have a higher ES than developing countries.Originality/valueFor the first time, the author uses the first-order Taylor series expansion to linearize the steady-state value of income per worker, as the author considers this approach to be relatively more straight-forward and tractable. Furthermore, the author estimates the equations using both cross-section and panel data techniques and employs the data-driven algorithm proposed by Phillips and Sul (2007) to classify countries.

AUTOMATION, PARTIAL AND FULL

When some steps of a complex, multi-step task are automated, the demand for human work in the remaining complementary sub-tasks goes up. In contrast, when the task is fully automated, the demand for human work declines. Upon aggregation to the macroeconomic scale, partial automatability of complex tasks creates a bottleneck of development, where further growth is constrained by the scarcity of essential human work. This bottleneck is removed once the tasks become fully automatable. Theoretical analysis using a two-level nested constant elasticity of substitution production function specification demonstrates that the shift from partial to full automation generates a non-convexity: humans and machines switch from complementary to substitutable, and the share of output accruing to human workers switches from an upward to a downward trend. This process has implications for inequality, the risk of technological unemployment, and the likelihood of a secular stagnation.