# Advances in Mathematical Finance and Application (AMFA)

Advances in Mathematical Finance and Application, Volume 4, Issue 2, Spring 2019

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## Application of Mathematics in Financial Management

نویسنده:
The Time Value of Money is a important concept in Financial Management. The Time Value of Money includes the concepts of future value and discounted value or present value. In the present article, the basic notions and illustrate with their application in the field of investment which is presented in the mathematical terms in form of theorems and we also presented the applications of some well known problems with the proof such as mortagage loan problem, investment in bond and an individual who plans to retire in certain years who plan for invest-ment for its future life. We also presented the application of calculus that is limit, derivative and integration in financial management.
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## Opaque Information, Deviation from Target Leverage and Speed of Adjustment

Information opacity leads to information asymmetry. In this situation, in providing their own financial needs, firms face limitations and inevitably provide their financial needs from the debt market by signalling private information to it. In addition, information opacity affects the leverage adjustment speed. This research investigates the effect of information opacity on deviation from target leverage and its’ adjustment speed during 2003 - 2017 in 131 firms listed in Tehran Stock Exchange. To estimate the research models, we use the regression analysis with panel data approach, the approach to control the effects of years and industries and the generalized method of moments with system estimator (system GMM). The research results show that the increase in information opacity increases (decreases) the positive (negative) deviation from target leverage. Also, research findings indicate that the increase in information opacity decreases the adjustment speed.
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## Free Cash Flow, Institutional Ownership and Long-Term Performance

Performance appraisal is a process which help shareholders make informed and optimal investment decisions. In recent decades, a long stream of research has devoted particular attention to the importance and impact of financial decisions on firm performance and firm value. The present study thus is primarily concerned with investigating the association between free cash flow and institutional ownership and long-term performance of the firms listed on the Tehran Stock Exchange over the period of 2012-2016. Moreover, firm size, financial leverage and sale grows serve as the control variables of the research. A number of 89 firms listed on the Tehran Stock Exchange were selected, and then the research hypotheses were tested using multivariate regression model based on panel data. The results reveal that firm long-term performance is not significantly correlated with free cash flow, yet it has a significant relationship with institutional ownership.
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## The Integration of Multi-Factor Model of Capital Asset Pricing and Penalty Function for Stock Return Evaluation

One of the main concerns of investors is the evaluation of the return on investment, which is conducted using various models such as the CAPM (single-factor model), Fama-French three/five-factor models, and Roy and Shijin’s six-factor model and other models known as multi-factor models. Despite the widespread use of these models, their major drawbacks include sensitivity to unexpected changes, sudden shocks, high turbulence of price bubble, and so on. To eliminate such negatives, the multi-factor model using the penalty function method is used, in which, instead of averaging, the optimization and avoidance of the effects of abnormal changes and other factors affecting the capital market are considered. In order to evaluate stock returns, it is possible to select effective factors, to simulate and develop a model appropriate to the conditions governing the capital market in Iran. In the present study, by forming portfolios of investments and identifying and refining effective factors, the classification and estimation of the hybrid model of penalty and multi-factor (P & PCA) functions were performed based on the functional data during 2007-2017. The results of this study indicated that the extensive use of the simulation algorithm for the penalty function in the form of P & PCA estimation method improves the efficiency of multi-factor methods in stock return evaluation, and that the use of the hybrid algorithm of penalty and multi-factor functions, compared to the exclusive use of multi-factor models, brings a higher accuracy in estimating stock returns.
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## On Vector Equilibrium Problem with Generalized Pseudomonotonicity

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash\$acute{'}\$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonotonicity for vector valued bifunctions is introduced. By using it some existence results for the vector equilibrium problem, in the setting of<br /> topological vector spaces, are presented. Some examples in order to illustrate the main results and compare them with the corresponding published results are furnished. Further, the compactness of the solution set of vector equilibrium problem is investigated.
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## Designing Native Decision-Making Model for Selecting Venture Capital Investment in Emerging Companies

Venture capital companies play an important role in the economy of countries and greatly influences economic and employment growth. VC is the provision of capital for companies and entrepreneurs that is prone to leaping and growing value and, of course, a lot of risk. However, the volume of venture capital in our country is far less than the economic capacity. Many of analysts consider having no model for venture capital in our country as the main reason for this. Therefore, the present study by the qualitative method aims to design decision-making native model for selecting venture capital investment in emerging companies. To achieve this goal, by collecting qualitative data through literature reviews and having deep interview with experts and venture capital firms, a native decision-making model for selecting venture capital in emerging companies is presented. The methodology of this research based on purpose, is fundamental and through the qualitative methods, thematic analysis method is used. Purposeful sampling method is used and interviewing experts continued to theoretical saturation level that means the number of selected samples includes 16 elites. The native decision-making model for selecting venture capital in emerging companies presented in this research has 16 main themes and 86 sub-themes.
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## Comparison of Public Investment Approaches on Social Welfare Function: A Case Study of Iran

The use of natural resource revenues for achievement of development has been a challenging issue for resource abundant countries. These challenges stem from the fact that incomes from natural resources are non-durable, unpredictable and uncertain. Different countries have pursued various approaches and tools for managing these revenues to avoid economic fluctuations. The international organizations and economic experts propose a diversification in the use of resource revenues through different approaches of public investment. Maximizing the social welfare function has become a common guideline for resource revenue management in resource-rich countries. This article investigates the effect of public investment approaches and their impacts on intergenerational social welfare function of Iran. To this end, the impact of two public investment approaches, namely Permanent Income Hypothesis (PIH) and Bird In Hand (BIH), was examined and compared on a certainty equivalent of social welfare function. Results of the simulation with Iran's economic data indicated substantial positive loss in welfare if switching to the BIH approach. Calculations show that the certainty equivalent of social welfare function for PIH and BIH is 786.3 and 444.3, respectively. PIH provides a higher welfare level for the Iranian economy.
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## Prediction the Return Fluctuations with Artificial Neural Networks' Approach

Time changes of return, inefficiency studies performed and presence of effective factors on share return rate are caused development modern and intelligent methods in estimation and evaluation of share return in stock companies. Aim of this research is prediction of return using financial variables with artificial neural network approach. Therefore, the statistical population of this study includes 120 listed companies in Tehran stock securities during 2005 to 2017. Independent variables in this research are market variables (Earning quality, free cash flow) and dependent variable is share return. The obtained outputs from estimation of the artificial neural networks and results obtained from estimation, using of this method with evaluation scales concerning random amount and comparing it with adjusted R, we found that there is meaningful relation between the associated variables and return. However, such network has the least error than other networks.