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Journal articles on the topic 'Fundamental Theorem of Finance'

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Published: 7 December 2024

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1

Brown, Martin, and Tomasz Zastawniak. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs." Annals of Finance 16, no. 3 (May 26, 2020): 423–33. http://dx.doi.org/10.1007/s10436-020-00367-z.

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2

Chernyi, A. S. "The vector stochastic integral in the first fundamental theorem of the mathematics of finance." Russian Mathematical Surveys 53, no. 4 (August 31, 1998): 866–67. http://dx.doi.org/10.1070/rm1998v053n04abeh000062.

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3

Guasoni, Paolo, Miklós Rásonyi, and Walter Schachermayer. "The fundamental theorem of asset pricing for continuous processes under small transaction costs." Annals of Finance 6, no. 2 (December 9, 2008): 157–91. http://dx.doi.org/10.1007/s10436-008-0110-x.

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4

BIELECKI, TOMASZ R., IGOR CIALENCO, ISMAIL IYIGUNLER, and RODRIGO RODRIGUEZ. "DYNAMIC CONIC FINANCE: PRICING AND HEDGING IN MARKET MODELS WITH TRANSACTION COSTS VIA DYNAMIC COHERENT ACCEPTABILITY INDICES." International Journal of Theoretical and Applied Finance 16, no. 01 (February 2013): 1350002. http://dx.doi.org/10.1142/s0219024913500027.

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In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.

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5

Teeple, Keisuke. "Surprise and default in general equilibrium." Theoretical Economics 18, no. 4 (2023): 1547–83. http://dx.doi.org/10.3982/te4943.

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I model an incomplete markets economy where unaware agents do not perceive all states of nature, so unintended default can occur when asset returns differ from what was perceived. The presence of default plays a crucial role in the proof of existence—particularly in economies where beliefs are biased—by removing perceived arbitrage opportunities with respect to delivery‐adjusted asset returns. The First Fundamental Welfare Theorem fails because of default and pecuniary inefficiencies, but the Second Fundamental Welfare Theorem holds for economies with no aggregate risk. Welfare is shown to not necessarily be monotonic in discovery or the increasing of awareness.

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6

ALLAJ, ERINDI. "IMPLICIT TRANSACTION COSTS AND THE FUNDAMENTAL THEOREMS OF ASSET PRICING." International Journal of Theoretical and Applied Finance 20, no. 04 (April 27, 2017): 1750024. http://dx.doi.org/10.1142/s0219024917500248.

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This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Implicit transaction costs are composed of two terms, one is able to capture the bid-ask spread, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having cádlág (right-continuous with left limits) and cáglád (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, cádlág and cáglád predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to cáglád predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with implicit transaction costs. To better understand how to apply the theory proposed we provide an example of an implicit transaction cost economy that is linear and nonlinear in the order size.

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7

Acciaio, B., M. Beiglböck, F. Penkner, and W. Schachermayer. "A MODEL-FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER-REPLICATION THEOREM." Mathematical Finance 26, no. 2 (December 6, 2013): 233–51. http://dx.doi.org/10.1111/mafi.12060.

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8

ALLEN, DOUGLAS W. "The Coase theorem: coherent, logical, and not disproved." Journal of Institutional Economics 11, no. 2 (February 28, 2014): 379–90. http://dx.doi.org/10.1017/s1744137414000083.

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Abstract:There exists a long line of challengers to the ‘Coase Theorem’. All of these rest on fundamental misconceptions of property rights, transaction costs, and their interaction. Here I examine two attacks that have gone unchallenged: one by Halpin, the other by Usher. I argue that both, in failing to either use or understand an adequate definition of transaction costs, fail to deliver a fatal blow to Coase's famous idea.

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9

FRAHM, GABRIEL. "CORRIGENDUM: “PRICING AND VALUATION UNDER THE REAL-WORLD MEASURE”." International Journal of Theoretical and Applied Finance 21, no. 04 (June 2018): 1892001. http://dx.doi.org/10.1142/s0219024918920012.

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In order to prove the third fundamental theorem of asset pricing for financial markets with infinite lifetime [G. Frahm (2016) Pricing and valuation under the real-world measure, International Journal of Theoretical and Applied Finance 19, 1650006], we shall assume that the discounted price process is locally bounded. Otherwise, some principal results developed by [F. Delbaen & W. Schachermayer (1997) The Banach space of workable contingent claims in arbitrage theory, Annales de l’Institut Henri Poincaré 1, 114–144] cannot be applied.

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10

Vazifedan, Mehdi, and Qiji Jim Zhu. "No-Arbitrage Principle in Conic Finance." Risks 8, no. 2 (June 19, 2020): 66. http://dx.doi.org/10.3390/risks8020066.

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In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid–ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “no-arbitrage” principle in financial models with the bid–ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

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11

Deepak B. Pachpatte. "Properties of some nonlinear partial dynamic equations on time scales." Malaya Journal of Matematik 1, no. 04 (October 1, 2013): 1–9. http://dx.doi.org/10.26637/mjm104/001.

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The aim of the present paper is to study some basic qualitative properties of solutions of certain nonlinear partial dynamic equations on time scales. The tools employed are application of Banach fixed point theorem and a variant of certain fundamental integral inequality with explicit estimates on time scales.

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12

Kühn, Christoph, and Alexander Molitor. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs." Finance and Stochastics 23, no. 4 (September 5, 2019): 1049–77. http://dx.doi.org/10.1007/s00780-019-00403-5.

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13

Karaś, Marek, and Anna Serwatka. "Discrete-time market models from the small investor point of view and the first fundamental-type theorem." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (December 1, 2017): 17–40. http://dx.doi.org/10.1515/aupcsm-2017-0002.

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Abstract In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with d risky assets), which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free.

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14

Obłój, Jan, and Johannes Wiesel. "A unified framework for robust modelling of financial markets in discrete time." Finance and Stochastics 25, no. 3 (June 14, 2021): 427–68. http://dx.doi.org/10.1007/s00780-021-00454-7.

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AbstractWe unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in finite discrete time. In particular, we prove a fundamental theorem of asset pricing and a superhedging theorem which encompass the formulations of Bouchard and Nutz [12] and Burzoni et al. [13]. In bringing the two streams of literature together, we examine and compare their many different notions of arbitrage. We also clarify the relation between robust and classical ℙ-specific results. Furthermore, we prove when a superhedging property with respect to the set of martingale measures supported on a set $\Omega $ Ω of paths may be extended to a pathwise superhedging on $\Omega $ Ω without changing the superhedging price.

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15

Gilboa, Itzhak, and Larry Samuelson. "What were you thinking? Decision theory as coherence test." Theoretical Economics 17, no. 2 (2022): 507–19. http://dx.doi.org/10.3982/te4707.

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Decision theory can be used to test the logic of decision making—one may ask whether a given set of decisions can be justified by a decision‐theoretic model. Indeed, in principal–agent settings, such justifications may be required—a manager of an investment fund may be asked what beliefs she used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain‐act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the fundamental theorem of finance (for the special case of a Bayesian agent) and revealed‐preference results.

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16

Schachermayer, Walter. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time." Mathematical Finance 14, no. 1 (January 2004): 19–48. http://dx.doi.org/10.1111/j.0960-1627.2004.00180.x.

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17

Mishra, Ravindra. "The Profound Nature of Derivatives and Integration: A Comprehensive Examination." Patan Prospective Journal 4, no. 01 (October 1, 2024): 103–9. http://dx.doi.org/10.3126/ppj.v4i01.70206.

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This article delves into the fundamental concepts of derivatives and integration, two core principles of calculus that govern a wide range of mathematical and real-world applications. Derivatives, which measure the rate of change of a function, and integration, which calculates accumulation and areas under curves, are essential tools in fields such as physics, economics, engineering, and finance. The article offers a detailed exploration of their mathematical definitions, key properties—including linearity, the product and chain rules, and the Fundamental Theorem of Calculus—and the diverse techniques used in integration. The practical applications of these concepts are also examined, with special emphasis on their role in modeling dynamic systems, optimizing processes, and solving real-world problems such as motion analysis, financial modeling, and economic optimization. Through in-depth discussion and examples, this comprehensive article bridges the theoretical underpinnings of derivatives and integration with their vast and critical uses in various scientific and economic disciplines.

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18

Evstigneev, Igor V., Klaus Schurger, and Michael I. Taksar. "On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang-Bang No-Arbitrage Criteria." Mathematical Finance 14, no. 2 (April 2004): 201–21. http://dx.doi.org/10.1111/j.0960-1627.2004.00189.x.

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19

FRAHM, GABRIEL, ALEXANDER JONEN, and RAINER SCHÜSSLER. "THE FUNDAMENTAL THEOREMS OF ASSET PRICING AND THE CLOSED-END FUND PUZZLE." International Journal of Theoretical and Applied Finance 22, no. 05 (August 2019): 1950025. http://dx.doi.org/10.1142/s0219024919500250.

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We propose a solution to the closed-end fund puzzle in financial markets without a free lunch with vanishing risk. Our results are consistent with both the time-series and the cross-sectional aspect of the closed-end fund puzzle. It turns out that a closed-end fund cannot exist if the fund manager is supposed to receive a fee although he is not able to find mispriced assets in the market. By contrast, a premium can typically be observed at the initial public offering because the fund manager has access to information that enables him to create a dominant strategy. As soon as this weak arbitrage opportunity evaporates, a premium can no longer occur. The reason why a premium quickly turns into a discount might be that the fund manager stops applying a superior trading strategy at some point in time. Another possibility is that abnormal profits are transient in a competitive financial market. In any case, when the fund manager is no longer willing or able to maintain a superior strategy, the fund must trade at a discount in order to compensate for his management fee.

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20

CHEN, GUAN-YU, KEN PALMER, and YUAN-CHUNG SHEU. "THE LEAST COST SUPER REPLICATING PORTFOLIO IN THE BOYLE–VORST MODEL WITH TRANSACTION COSTS." International Journal of Theoretical and Applied Finance 11, no. 01 (February 2008): 55–85. http://dx.doi.org/10.1142/s0219024908004725.

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Boyle and Vorst work in the framework of the binomial model and derive self-financing strategies perfectly replicating the final payoffs to long and short positions in call and put options, assuming proportional transactions costs on trades in the stock and no transactions costs on trades in the bond. Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. Bensaid et al. gave conditions under which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. These results were generalized by Stettner, Rutkowski and Palmer to the case of asymmetric transaction costs. In this paper, we first determine the number of replicating portfolios and then compute the least cost super replicating portfolio for any contingent claim in a one-period binomial model. By using the fundamental theorem of linear programming, we show that there are only finitely many possibilities for a least cost super replicating portfolio for any contingent claim in a two-period binomial model. As an application of our results, we give an example in which we compute the least cost super replicating portfolio for a butterfly spread in a two-period model.

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21

Kapeliushnikov, R. I. "Multihanded Adam Smith (Part two)." Voprosy Ekonomiki, no. 11 (November 9, 2023): 123–40. http://dx.doi.org/10.32609/0042-8736-2023-11-123-140.

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The paper analyzes the metaphor of “an invisible hand”, which was introduced two and a half centuries ago by Adam Smith (1723—1790) and which eventually became the central concept of the modern economics. The second part examines the origin and history of the reception of Smith’s metaphor at various stages of the evolution of economic thought. Paradoxically, it gained wide popularity only since the middle of the 20th century due to its mention in the famous textbook by P. Samuelson “Economics”. In the interpretation of this metaphor by modern economists, two traditions exist — neoclassical and Austrian. In mainstream, Smith’s “invisible hand” is identified with the First Fundamental Theorem of welfare economics, which looks like an anachronism. There are more grounds for the convergence of the concepts of “an invisible hand” and “spontaneous order”, from which the Austrian school proceeds. Smith almost accidentally stumbled upon a figurative expression which turned out to be heuristically extremely productive and has become firmly embedded in the lexicon of many modern disciplines — from economics to the philosophy of science

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22

Majid, Mohd Azlan Abdul, Faridah Pardi, Afizan Amer, Nor’ Azurah Md Kamdari, and Sarah Mardhiah Selamat. "Air Passengers Vertex Curve Theorem - Evidence from ASEAN Countries." Asian Economic and Financial Review 9, no. 3 (March 27, 2019): 329–38. http://dx.doi.org/10.18488/journal.aefr.2019.93.329.338.

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This study examines new generic hypotheses and theorems of the aviation industry’s model for air passengers for ASEAN countries. A static panel data model consists of a simple panel unit and root and cointegration tests were established for the period from 1997 to 2016. Initially, we hypothesized that internet connection, income level, tax and tourism expenditures all have significant impacts on the volume of air passengers in ASEAN countries. Our main findings showed that gross national income (GNI) has a positive significant impact on air passengers’ volume and it is also the peak of the vertex. In addition, according to the hypothesized vertex theorem, the policy-impact of taxation on air passenger volume showed a weak significance, while the digital-impact hypothesis of broadband and mobile technology exhibited a mediocre and substitution impact. Our conclusion from the findings highlighted that fundamentals of domestic economic growth should be strengthened in order to increase internal economic capacity. By achieving this, the volume of the air passenger could be doubled and therefore would bring back a growth of income and prosperity to the nation, particularly in the ASEAN market.

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23

Staum, Jeremy. "Fundamental Theorems of Asset Pricing for Good Deal Bounds." Mathematical Finance 14, no. 2 (April 2004): 141–61. http://dx.doi.org/10.1111/j.0960-1627.2004.00186.x.

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24

Saijo, Tatsuyoshi, and Takehiko Yamato. "Fundamental impossibility theorems on voluntary participation in the provision of non-excludable public goods." Review of Economic Design 14, no. 1-2 (December 1, 2009): 51–73. http://dx.doi.org/10.1007/s10058-009-0100-0.

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25

Jacod, J., and A. N. Shiryaev. "Local martingales and the fundamental asset pricing theorems in the discrete-time case." Finance and Stochastics 2, no. 3 (May 1, 1998): 259–73. http://dx.doi.org/10.1007/s007800050040.

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26

Bolthausen, Erwin, and Mario V. Wüthrich. "BERNOULLI'S LAW OF LARGE NUMBERS." ASTIN Bulletin 43, no. 2 (May 2013): 73–79. http://dx.doi.org/10.1017/asb.2013.11.

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AbstractThis year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science. We review and comment on his original proof.

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27

Chen, Yongzhao, Ka Chun Cheung, Sheung Chi Phillip Yam, Fei Lung Yuen, and Jia Zeng. "On the Diversification Effect in Solvency II for Extremely Dependent Risks." Risks 11, no. 8 (August 4, 2023): 143. http://dx.doi.org/10.3390/risks11080143.

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In this article, we investigate the validity of diversification effect under extreme-value copulas, when the marginal risks of the portfolio are identically distributed, which can be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. We show that Value-at-Risk (V@R) under extreme-value copulas is asymptotically subadditive for marginal risks with finite mean, while it is asymptotically superadditive for risks with infinite mean. Our major findings enrich and supplement the context of the second fundamental theorem of quantitative risk management in existing literature, which states that V@R of a portfolio is typically non-subadditive for non-elliptically distributed risk vectors. In particular, we now pin down when the V@R is super or subadditive depending on the heaviness of the marginal tail risk. According to our results, one can take advantages from the diversification effect for marginal risks with finite mean. This justifies the standard formula for calculating the capital requirement under Solvency II in which imperfect correlations are used for various risk exposures.

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28

HAYWARD, SERGE. "PREDICTING PRICES OF FINANCIAL ASSETS: FROM CLASSICAL ECONOMICS TO INTELLIGENT FINANCE." New Mathematics and Natural Computation 07, no. 02 (May 2011): 229–47. http://dx.doi.org/10.1142/s1793005711001901.

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Determining the circumstances under which it is possible to make any sort of prediction is a fundamental question in financial research. The presence of complex and robust statistical characteristics, exhibited by most financial time series, raise doubts on the simple relationship between information and price changes, as implied by the efficient market hypothesis. In this paper, we consider the main competing economic hypotheses and examine different approaches for learning the price behaviour in financial markets. Our analysis reveals the need to approach the problem from a new perspective. In financial markets, traders are not only adapting, but also determine and form the economic mechanism essentially by their actions. In these settings, financial markets are evolutionary structures of competing trading strategies; prices in such markets are driven endogenously by the induced expectations. A combination of economics, computer and cognitive science in cross-disciplinary study of intelligent finance, which aims to explore information about financial markets from multiple perspectives, is expected to expand the boundary of pure economic analysis.

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29

Selivanova, Olga. "EDMONDO DE AMICIS’ BOOKS IN THE COLLECTION OF THE HERZEN STATE PEDAGOGICAL UNIVERSITY’S FUNDAMENTAL LIBRARY." Children's Readings: Studies in Children's Literature 21, no. 1 (2022): 265–84. http://dx.doi.org/10.31860/2304-5817-2022-1-21-265-284.

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The article provides an overview of the works of E. De Amicis published in Russian and stored in the collections of the Fundamental Library of the Herzen State Pedagogical University. Most of the publications contain certain book signs, by which you can find out the history of the existence of each copy and trace the path of their entry into the library. The books of E. De Amicis were very popular, therefore they were present in almost every library oriented to the children’s readership: libraries of state institutions (for example, the library of employees in the Ministry of Finance, the library for employees of the State Bank) and various educational institutions (schools, colleges, institutes), public children’s libraries and personal collections. Recommendations for the purchase of books by E. De Amicis for reading to children came from both official departments of the Ministry of Public Education and specialists in children’s literature as part of various indexes and on the pages of periodicals. The main attention is paid to translations and editions of the most popular story “Cuore”, as well as editions of individual stories extracted from it. Their number was difficult to name already at the beginning of the 20 th century.

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30

Pronko, Lyudmila, Tatyana Kolesnik, and Oksana Samborska. "Essence and Concept of Capitalization of Enterprises its Types and Methods of Evaluation." European Journal of Sustainable Development 10, no. 1 (February 1, 2021): 551. http://dx.doi.org/10.14207/ejsd.2021.v10n1p551.

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The historical aspect of the development of scientists' views on the company's capitalization is studied in the work, the stages of development of the concept of cost-oriented management are determined. The role and place of market capitalization in the system of indicators of cost-oriented management are determined, modern methodical approaches to the assessment of the value of the enterprise taking into account the indicator of market capitalization are given. The fundamental differences between the areas of application of indicators of market value of the enterprise and market capitalization are established. The current problems of the Ukrainian economy that limit the widespread use of market capitalization in the valuation of companies are outlined, and proposals are made on the feasibility of valuing Ukrainian companies in terms of real capitalization. The importance of enterprise capitalization in the development of a market economy is emphasized. The evolution of the views of foreign scientists on the capitalization of enterprises has been studied. It is established that the economic essence of the capitalization of enterprises, as well as any asset, is the present value of future income generated by this asset. Bringing future income to the present is a process of discounting. The theory of capitalization of the company in its modern context began to be formed by neoclassical economists from the end of the XIX century. and gained popularity in the second part XX century. The theory of capitalization has given impetus to well-known neoclassical theories of corporate finance, such as the irrelevance theorem, risk theory, investment portfolio optimization theory, arbitrage pricing theory, and so on. It is established that according to the theory of capitalization, the capitalization of the enterprise and the market value of the enterprise are identical concepts, although the methods of their calculation differ. The theory of capitalization has given impetus to the development of many modern financial theories, which are currently under development and improvement.

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Мажгихова, М. Г. "The Cauchy Problem for the Delay Differential Equation with Dzhrbashyan – Nersesyan Fractional Derivative." Вестник КРАУНЦ. Физико-математические науки, no. 1 (April 17, 2023): 98–107. http://dx.doi.org/10.26117/2079-6641-2023-42-1-98-107.

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Последние десятилетия количество работ, посвященных исследованию задач для дифференциальных уравнений дробного порядка, заметно растет. Интерес исследователей вызван тем, что количество областей науки, в которых используются уравнения, содержащие дробные производные, варьируется от биологии и медицины до теории управления, инженерии, финансов, а также оптики, физики и так далее. Включение запаздывания в уравнение дробного порядка существенно влияет на ход процесса, описываемого этим уравнением, так как неизвестная функция задается при различных значениях аргумента, что вносит эффект предыстории в уравнение. Поэтому, математические модели, содержащие дробный оператор и запаздывающий аргумент, более точны, чем модели, содержащие производные целого порядка. В данной работе исследуется задача Коши для линейного обыкновенного дифференциального уравнения с запаздывающим аргументом c оператором дробного дифференцирования Джрбашяна – Нерсесяна, обобщающим известные дробные операторы Римана – Лиувилля и Герасимова – Капуто. Результаты работы получены с использованием методов теории целого и дробного исчислений, методов теории дифференциальных уравнений с запаздывающим аргументом, метода специальных функций. В работе доказывается теорема о справедливости аналога формулы Лагранжа. Также доказано, что специальная функция Wγm(t), которая, в свою очередь, определяется через обобщенную функцию Миттаг – Леффлера (или функция Прабхакара), удовлетворяет уравнению и условиям, сопряженным исследуемому, и является фундаментальным решением рассматриваемого уравнения. Сформулирована и доказана теорема существования и единственности решения начальной задачи. Решение поставленной задачи выписано в терминах специальной функции Wν(t). In recent, the number of works devoted to the study of problems for fractional order differential equations is growing noticeably. The interest of researchers is due to the fact that the number of areas of science in which equations containing fractional derivatives are used varies from biology and medicine to control theory, engineering, finance, as well as optics, physics, and so on. The inclusion of delay in the fractional order equation significantly affects the course of the process described by this equation, since the unknown function is given for different values of the argument, which includes a history effect into the equation. Therefore, mathematical models containing a fractional operator and a delay argument are more accurate than models containing integer derivatives. In this paper, we study the Cauchy problem for a linear ordinary delay differential equation with the Dzhrbashyan – Nersesyan fractional differentiation operator, which is generalizing the Riemann – Liouville and Gerasimov – Caputo fractional operators. The results of the work are obtained using the methods of the theory of integer and fractional calculus, methods of the theory of delay differential equations, the method of special functions. In this paper proves a theorem on the validity of an analogue of the Lagrange formula. It is also proved that the special function Wγm(t), which is defined in terms of the generalized Mittag-Leffler function (or the Prabhakar function), satisfies the equation and conditions associated with the one under study, and is the fundamental solution of the considered equation. The main result is that the existence and uniqueness theorem to the initial value problem is proved. The solution to the problem is written out in terms of the special function Wν(t).

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32

Wagner, Jack. "Barrow's Fundamental Theorem." College Mathematics Journal 32, no. 1 (January 2001): 58. http://dx.doi.org/10.2307/2687226.

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Aharoni, Amikam. "Brown’s “fundamental theorem” revisited." Journal of Applied Physics 90, no. 9 (November 2001): 4645–50. http://dx.doi.org/10.1063/1.1407313.

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Sobczyk, Garret, and Omar León Sánchez. "Fundamental Theorem of Calculus." Advances in Applied Clifford Algebras 21, no. 1 (July 30, 2010): 221–31. http://dx.doi.org/10.1007/s00006-010-0242-8.

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35

Loya, Paul. "Green's Theorem and the Fundamental Theorem of Algebra." American Mathematical Monthly 110, no. 10 (December 2003): 944. http://dx.doi.org/10.2307/3647967.

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Loya, Paul. "Green's Theorem and the Fundamental Theorem of Algebra." American Mathematical Monthly 110, no. 10 (December 2003): 944–46. http://dx.doi.org/10.1080/00029890.2003.11920036.

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Antoine, Bertille, Kevin Proulx, and Eric Renault. "Pseudo-True SDFs in Conditional Asset Pricing Models*." Journal of Financial Econometrics 18, no. 4 (September 18, 2018): 656–714. http://dx.doi.org/10.1093/jjfinec/nby017.

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Abstract This article is motivated by the need to bridge some gap between modern asset pricing theory and recent developments in econometric methodology. While asset pricing theory enhances the use of conditional pricing models, econometric inference of conditional models can be challenging due to misspecification or weak identification. To tackle the case of misspecification, we utilize the conditional Hansen and Jagannathan (1997) (HJ) distance as studied by Gagliardini and Ronchetti (2016), but we set the focus on interpretation and estimation of the pseudo-true value defined as the argument of the minimum of this distance. While efficient Generalized Method of Moments (GMM) has no meaning for estimation of a pseudo-true value, the HJ-distance not only delivers a meaningful loss function, but also features an additional advantage for the interpretation and estimation of managed portfolios whose exact pricing characterizes the pseudo-true pricing kernel (stochastic discount factor (SDF)). For conditionally affine pricing kernels, we can display some managed portfolios which are well-defined independently of the pseudo-true value of the parameters, although their exact pricing is achieved by the pseudo-true SDF. For the general case of nonlinear SDFs, we propose a smooth minimum distance (SMD) estimator (Lavergne and Patilea, 2013) that avoids a focus on specific directions as in the case of managed portfolios. Albeit based on kernel smoothing, the SMD approach avoids instabilities and the resulting need of trimming strategies displayed by classical local GMM estimators when the density function of the conditioning variables may take arbitrarily small values. In addition, the fact that SMD may allow fixed bandwidth asymptotics is helpful regarding the curse of dimensionality. In contrast with the true unknown value for a well-specified model, the estimated pseudo-true value, albeit defined in a time-invariant (unconditional) way, may actually depend on the choice of the state variables that define fundamental factors and their scaling weights. Therefore, we may not want to be overly parsimonious about the set of explanatory variables. Finally, following Antoine and Lavergne (2014), we show how SMD can be further robustified to deal with weaker identification contexts. Since SMD can be seen as a local extension of the method of jackknife GMM (Newey and Windmeijer, 2009), we characterize the Gaussian asymptotic distribution of the estimator of the pseudo-true value using classical U-statistic theorems.

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38

Krantz, Steven. "How Fundamental is the Fundamental Theorem of Algebra?" Mathematics Magazine 93, no. 2 (March 14, 2020): 139–42. http://dx.doi.org/10.1080/0025570x.2020.1704614.

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39

Cordova, Salvador. "Fisher’s Fundamental Theorem of Natural Selection Isn’t Fundamental After All." Communications of the Blyth Institute 2, no. 2 (August 1, 2020): 25–34. http://dx.doi.org/10.33014/issn.2640-5652.2.2.cordova.1.

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Fisher’s Fundamental Theorem of Natural Selection (FTNS) was called “biology’s central theorem” (Fisher, 1930, pgs. 36–37; Brockman, 2011; Royal Society, 2020). FTNS might possibly have been accorded this status for decades because Fisher himself declared his own theorem to be fundamental to biology (Fisher, 1930, pgs. 36–37). However, the idea that Fisher’s theorem is biology’s central theorem is by-and-large a myth promoted by popu- lar science writers like Richard Dawkins (Brockman, 2011). Joseph Felsenstein, when delivering the 2018 Fisher Memorial Lecture declared that FTNS was “alas, not so fundamental” (Felsenstein, 2018; Felsenstein, 2017, pg. 94. One may be hard-pressed to find a biology textbook or biology student who can explain how FTNS helps them understand biology. Even the meaning and proof of the FTNS have re- mained contentious even to this day (Price, 1972; Basener and Sanford, 2018). Not only does FTNS do little to nothing to explain biological evolution, but like most population genetic and evolutionary literature, FTNS relies on a definition of fit- ness in terms of population growth rates rather than the biophysical notions of fitness which are more in line with the common-sense intuitions of the medical and engineering communities. From the perspective of the biophysical (rather than the population growth) notion of fitness, natural selection might be more accurately described as an agent against the increase of complexity rather than an agent for it. Thus, metaphorically speaking, some sort of anti-Weasel model of natural selection might better describe how selection actu- ally works in nature rather than Dawkins’ Weasel or other man-made genetic algorithms. However, the main focus of this communication is to pro- vide some pedagogical insights through simple numerical illustrations of Fisher’s Theorem. The hope is that this will show the general irrelevance of FTNS to the question of the evolution of complexity by means of natural selection, and thus show that Fisher’s Theorem is not so fundamental after all.

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40

Hirschhorn, Michael D. "The Fundamental Theorem of Algebra." College Mathematics Journal 29, no. 4 (September 1998): 276. http://dx.doi.org/10.2307/2687681.

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Winter, Sidney G. "Winter's Fundamental Selection Theorem: Reply." Quarterly Journal of Economics 105, no. 4 (November 1990): 1075. http://dx.doi.org/10.2307/2937888.

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Hirschhorn, Michael D. "The Fundamental Theorem of Algebra." College Mathematics Journal 29, no. 4 (September 1998): 276–77. http://dx.doi.org/10.1080/07468342.1998.11973954.

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43

Diamantidis, Clarissa Jonas. "A Fundamental Theorem of Telehealth." Advances in Chronic Kidney Disease 24, no. 1 (January 2017): 4–5. http://dx.doi.org/10.1053/j.ackd.2016.11.001.

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44

Hilgert, Joachim, and Karl H. Hofmann. "On Sophus Lie's fundamental theorem." Journal of Functional Analysis 67, no. 3 (July 1986): 293–319. http://dx.doi.org/10.1016/0022-1236(86)90028-5.

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45

Perrucci, Daniel, and Marie-Françoise Roy. "Quantitative fundamental theorem of algebra." Quarterly Journal of Mathematics 70, no. 3 (May 15, 2019): 1009–37. http://dx.doi.org/10.1093/qmath/haz008.

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Abstract Using subresultants, we modify a real-algebraic proof due to Eisermann of the fundamental theorem of Algebra (FTA) to obtain the following quantitative information: in order to prove the FTA for polynomials of degree d, the intermediate value theorem (IVT) is required to hold only for real polynomials of degree at most d2. We also explain that the classical proof due to Laplace requires IVT for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.

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Park, Chull, David Skoug, and Lawrence Smolowitz. "Fundamental theorem of Wiener calculus." International Journal of Mathematics and Mathematical Sciences 13, no. 3 (1990): 443–52. http://dx.doi.org/10.1155/s0161171290000667.

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In this paper we define and develop a theory of differentiation in Wiener spaceC[0,T]. We then proceed to establish a fundamental theorem of the integral calculus forC[0,T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional. Secondly, we show that certain functionals defined onC[0,T]are equal to the indefinite integral of their Wiener derivative.

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CHILCOTE, RONALD H. "Perspectivas do capitalismo e do socialismo na busca de uma teoria de classe do estado e da democracia." Brazilian Journal of Political Economy 10, no. 4 (December 1990): 560–79. http://dx.doi.org/10.1590/0101-31571990-0545.

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RESUMO A crise da ciência política contemporânea e da ciência social, em geral, reflete a crise tanto do capitalismo quanto do socialismo. A busca de alternativas teóricas para resolver a crise envolveu um redirecionamento e não uma nova direção. Este artigo primeiro examina várias pós-formas de sociedade, especificamente pós-liberalismo, pós-imperialismo e pós-marxismo e afirma que, embora essas concepções possam ser inovadoras e provocativas, elas não permitem a formação de novos paradigmas. Em segundo lugar, o artigo examina criticamente os principais temas da década de 1990 e conclui com a observação de que os intelectuais divergem sobre a direção do desenvolvimento, uma vez que as questões se tornam de preferência fundamental para o capitalismo ou o socialismo; sobre questões do Estado por causa do uso de análises de classe ou não de classe; e sobre questões de socialismo e democracia por causa de sua inclinação a favorecer formas indiretas ou diretas de participação no processo político. Assim, a preferência pelo capitalismo ou pelo socialismo pode moldar ideais e distorcer realidades, de modo que a produção de novas ideias não pode ser outra coisa que a reprodução de velhas ideias sob uma nova roupagem.

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Fu, Yaoshun, and Wensheng Yu. "Formalization of the Equivalence among Completeness Theorems of Real Number in Coq." Mathematics 9, no. 1 (December 25, 2020): 38. http://dx.doi.org/10.3390/math9010038.

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The formalization of mathematics based on theorem prover becomes increasingly important in mathematics and computer science, and, particularly, formalizing fundamental mathematical theories becomes especially essential. In this paper, we describe the formalization in Coq of eight very representative completeness theorems of real numbers. These theorems include the Dedekind fundamental theorem, Supremum theorem, Monotone convergence theorem, Nested interval theorem, Finite cover theorem, Accumulation point theorem, Sequential compactness theorem, and Cauchy completeness theorem. We formalize the real number theory strictly following Landau’s Foundations of Analysis where the Dedekind fundamental theorem can be proved. We extend this system and complete the related notions and properties for finiteness and sequence. We prove these theorems in turn from Dedekind fundamental theorem, and finally prove the Dedekind fundamental theorem by the Cauchy completeness theorem. The full details of formal proof are checked by the proof assistant Coq, which embodies the characteristics of reliability and interactivity. This work can lay the foundation for many applications, especially in calculus and topology.

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Chemosit, Jephania, and Gerald Atheru. "Financial Leverage and Performance of the Energy and Petroleum Sector Companies Listed in the Nairobi Securities Exchange." International Journal of Current Aspects in Finance, Banking and Accounting 3, no. 2 (November 10, 2021): 113–28. http://dx.doi.org/10.35942/ijcfa.v3i2.208.

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Financial leverage and financial performance are fundamental issues in corporate finance. In Kenya, some companies listed at the Nairobi Securities Exchange have had performance improvement. However, most of them have experienced declining fortunes which has been attributed to the fact that corporate managers another practitioner lack adequate guidance required to attain optimal financing decisions. Financial leverage comprises of loans and other forms of debts where the proceeds from these loans are reinvested to earn higher return than the cost of loans. Financial use is the company's capacity to utilization of settled money related charges to amplify the impacts of changes in the profit before premium and duty on the company's income per share. The extent of obligation to value is a vital decision for corporate supervisors. The poor performance of Energy and Petroleum sector companies is of great concern. Financial leverage ranges from debt ratio, debt/equity ratio and interest coverage ratio which are vital since they directly affect the financial performance of firms. The general objective as to determine the effect of financial leverage on the financial performance of energy and petroleum sector companies listed in the NSE. While the specific objectives were; to establish the effect of debt ratio, debt -equity ratio and interest coverage ratio on financial performance of energy and petroleum sector companies recorded in the NSE. The research was anchored on the following theories: Modigliani-Miller theorem, Pecking Order Theory and Trade-off Theory. The empirical literature review was based on the three objectives of the study and gaps established. The study adopted a descriptive research design. Management of all the 5 energy and petroleum companies listed with the NSE was involved in the study which mainly used secondary data to conclude. Data was analyzed using regression analysis. Analyzed data was presented using tables. Confidence interval of 95% was used by the researcher. The study adopted a multiple regression model (Y = β0 + β1X1 + β2X2 + β3X3 +ε). The findings indicate that the independent variables Debt ratio, Debt to Equity ratio and interest cover ratio affected the financial performance of the firms in the Energy and petroleum sector. Their effect was up to 75.4%. Debt ratio and Debt to Equity ratio had a positive relationship whereas Interest cover ratio had a negative relationship to the firms in the Energy and petroleum sector listed in the NSE. This study recommends that the firms handle their capital structure decisions prudently as the changes in the factors like Debt ratio, Debt to Equity ratio and Interest cover ratio enhance profitability of firms when prudently employed and hence affect the performance of Energy and petroleum firms listed at the Nairobi Securities Exchange. This study also recommends that firms control the amount of interest expense since an increase in interest expense has an effect in that it reduces the financial performance of firms in the Energy and petroleum sector listed in the NSE.

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Liu, Dan. "Distribution of Prime Numbers Fundamental Theorem." Bulletin of Mathematical Sciences and Applications 3 (February 2013): 45–48. http://dx.doi.org/10.18052/www.scipress.com/bmsa.3.45.

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In 1849, the German mathematician Gauss large average distribution density of primesnear x. Based on the density of the Gauss proposed regional distribution of prime numbers theorem.And regional distribution of prime numbers theorem proved easy to understand way. Thefundamental theorem to obtain the distribution of prime numbers. Thus proving that a new primenumber theorem. Therefore gives the details of the calculation.

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