scholarly journals The arbitrage In Securities Market Model And Some There Properties

2021 ◽  
Vol 26 (4) ◽  
pp. 542-549
Author(s):  
Adel Murtda Al-awci ◽  
Noori F. Al-Mayahi
Keyword(s):  
Financial Markets ◽  
Linear Topological Space ◽  
Securities Market ◽  
Market Model ◽  
Separation Theorems ◽  
Topological Spaces ◽  
No Arbitrage ◽  
Mathematical Formulas ◽  
Economic Balance ◽  
Necessary And Sufficient

The  applications of functional analysis in economics began worked out since the  by presenting theoretical studies related to the development and balance of financial  markets by building mathematical models with linear topological space , describing and defining the economic balance of the stock market in mathematical formulas and terms , and then using the theorems of  linear topological spaces such as Han's theorems . Banach , separation theorems  , open function theorem ,closed statement theorem and so on to create the necessary and sufficient condition to make the market model achieve viability , achieve no arbitrage , and not recognize No free Lunches                                                                                                                             

scholarly journals Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 868
Author(s):  
Salvador Cruz Rambaud
Keyword(s):  
Financial Markets ◽  
Preference Relation ◽  
General Setting ◽  
Linear Topological Space ◽  
Point Of View ◽  
No Arbitrage ◽  
Algebraic Properties ◽  
Algebraic Concepts ◽  
Probabilistic Point ◽  
Absence Of Arbitrage

Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price p i to the marketed claim m i . The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory.

scholarly journals Agent-based risk management – a regulatory approach to financial markets

2015 ◽  
Vol 42 (5) ◽  
pp. 780-820 ◽  
Author(s):  
Thomas Theobald
Keyword(s):  
Financial Markets ◽  
Behavioral Model ◽  
Capital Requirements ◽  
Regulatory Framework ◽  
Market Model ◽  
Content Type ◽  
Agent Based ◽  
No Arbitrage ◽  
Market Participants ◽  
Regulatory Approach

Purpose – The purpose of this paper is to provide market risk calculation for an equity-based trading portfolio. Instead of relying on the purely stochastic internal model method which banks currently apply in line with the Basel regulatory requirements, the author also propose including alternative price mechanisms from the financial literature in the regulatory framework. Design/methodology/approach – For this purpose, a financial market model with heterogeneous agents is developed, capturing the realistic feature that parts of the investors do not follow the assumption of no arbitrage, but are motivated by behavioral heuristics instead. Findings – Although both the standard stochastic and the behavioral model are restricted to a calibration including the last 250 trading days, the latter is able to capitalize possible turbulence on financial markets and likewise the well-known phenomenon of excess volatility – even if the last 250 days reflect a non-turbulent market. Practical implications – Thus, including agent-based models in the regulatory framework could create better capital requirements with respect to their level and counter-cyclicality. Originality/value – This in turn could reduce the extent to which bubbles arise, since market participants would have to anticipate comprehensively the costs of such bubbles bursting. Furthermore, a key ratio is deduced from the agent-based construction to lower the influence of speculative derivatives.

Real-Estate Derivatives

2017 ◽  
Author(s):  
Radu S. Tunaru
Keyword(s):  
Real Estate ◽  
Financial Markets ◽  
Investment Banks ◽  
Financial Instruments ◽  
Stress Tests ◽  
Real World Data ◽  
No Arbitrage ◽  
New Frontier ◽  
Property Price ◽  
Comparative Description

This book brings together the latest concepts and models in real-estate derivatives, the new frontier in financial markets. The importance of real-estate derivatives in managing property price risk that has destabilized economies frequently in the last hundred years has been brought into the limelight by Robert Shiller over the last three decades. In spite of his masterful campaign for the introduction of real-estate derivatives, these financial instruments are still in a state of infancy. This book aims to provide a state-of-the-art overview of real-estate derivatives at this moment in time, covering the description of these financial products, their applications, and the most important models proposed in the literature in this area. In order to facilitate a better understanding of the situations when these products can be successfully used, ancillary topics such as real-estate indices, mortgages, securitization, and equity release mortgages are also discussed. The book is designed to pay attention to the econometric aspects of realestate index prices, time series, and also to financial engineering no-arbitrage principles governing pricing of derivatives. The emphasis is on understanding the financial instruments through their mechanics and comparative description. The examples are based on real-world data from exchanges or frommajor investment banks or financial houses in London. The numerical analysis is easily replicable with Excel and Matlab. This is the most advanced published book in this area, combining practical relevance with intellectual rigour. Real-estate derivatives will become important for managing macro risks in order to pass stress tests imposed by regulators.

scholarly journals International Liquidity and Exchange Rate Dynamics *

2015 ◽  
Vol 130 (3) ◽  
pp. 1369-1420 ◽  
Author(s):  
Xavier Gabaix ◽  
Matteo Maggiori
Keyword(s):  
Exchange Rate ◽  
Financial Markets ◽  
Exchange Rates ◽  
Capital Flows ◽  
Risk Sharing ◽  
Market Model ◽  
International Liquidity ◽  
Balance Sheets ◽  
Macroeconomic Analysis ◽  
International Pricing

Abstract We provide a theory of the determination of exchange rates based on capital flows in imperfect financial markets. Capital flows drive exchange rates by altering the balance sheets of financiers that bear the risks resulting from international imbalances in the demand for financial assets. Such alterations to their balance sheets cause financiers to change their required compensation for holding currency risk, thus affecting both the level and volatility of exchange rates. Our theory of exchange rate determination in imperfect financial markets not only helps rationalize the empirical disconnect between exchange rates and traditional macroeconomic fundamentals, it also has real consequences for output and risk sharing. Exchange rates are sensitive to imbalances in financial markets and seldom perform the shock absorption role that is central to traditional theoretical macroeconomic analysis. Our framework is flexible; it accommodates a number of important modeling features within an imperfect financial market model, such as nontradables, production, money, sticky prices or wages, various forms of international pricing-to-market, and unemployment.

scholarly journals ‎INSERTION OF A CONTRA-CONTINUOUS FUNCTION BETWEEN TWO ‎‎COMPARABLE CONTRA-$\alpha-$CONTINUOUS (CONTRA-$C-$CONTINUOUS) FUNCTIONS

2019 ◽  
pp. 13
Author(s):  
Majid Mirmiran ◽  
Binesh Naderi
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

‎A necessary and sufficient condition in terms of lower cut sets ‎are given for the insertion of a contra-continuous function ‎between two comparable real-valued functions on such topological ‎spaces that kernel of sets are open‎. 

scholarly journals An Interval of No-Arbitrage Prices in Financial Markets with Volatility Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hanlei Hu ◽  
Zheng Yin ◽  
Weipeng Yuan
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Stock Price ◽  
Contingent Claims ◽  
Price Dynamics ◽  
Complex Situation ◽  
No Arbitrage ◽  
Price Process ◽  
Arbitrage Opportunities

In financial markets with volatility uncertainty, we assume that their risks are caused by uncertain volatilities and their assets are effectively allocated in the risk-free asset and a risky stock, whose price process is supposed to follow a geometric G-Brownian motion rather than a classical Brownian motion. The concept of arbitrage is used to deal with this complex situation and we consider stock price dynamics with no-arbitrage opportunities. For general European contingent claims, we deduce the interval of no-arbitrage price and the clear results are derived in the Markovian case.

Monotone and E-Schauder Bases of Subspaces

1968 ◽  
Vol 20 ◽  
pp. 233-241 ◽  
Author(s):  
John P. Russo
Keyword(s):  
Normed Linear Space ◽  
Linear Span ◽  
Linear Topological Space ◽  
Principal Result ◽  
Schauder Basis ◽  
Topological Spaces ◽  
Dense Subspace ◽  
Closed Linear Span ◽  
Whole Space ◽  
Schauder Bases

The notions of monotone bases and bases of subspaces are well known in a normed linear space setting and have obvious extensions to pseudo-metrizable linear topological spaces. In this paper, these notions are extended to arbitrary linear topological spaces. The principal result gives a list of properties that are equivalent to a sequence (Mi) of complete subspaces being an e-Schauder basis of subspaces for the closed linear span of . A corollary of this theorem is the fact that an e-Schauder basis for a dense subspace of a linear topological space is an e-Schauder basis for the whole space.

Left Cauchy Integral Bases in Linear Topological Spaces

1970 ◽  
Vol 13 (4) ◽  
pp. 431-439 ◽  
Author(s):  
James A. Dyer
Keyword(s):  
Linear Topological Space ◽  
Integral Representations ◽  
Topological Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Natural Analogue ◽  
Cauchy Integral ◽  
Integral Basis ◽  
Integral Bases ◽  
Definition Of

The purpose of this paper is to consider a representation for the elements of a linear topological space in the form of a σ-integral over a linearly ordered subset of V; this ordered subset is what will be called an L basis. The formal definition of an L basis is essentially an abstraction from ideas used, often tacitly, in proofs of many of the theorems concerning integral representations for continuous linear functionals on function spaces.The L basis constructed in this paper differs in several basic ways from the integral basis considered by Edwards in [5]. Since the integrals used here are of Hellinger type rather than Radon type one has in the approximating sums for the integral an immediate and natural analogue to the partial sum operators of summation basis theory.

scholarly journals Metrisation of Moore spaces and abstract topological manifolds

1997 ◽  
Vol 56 (3) ◽  
pp. 395-401 ◽  
Author(s):  
David L. Fearnley
Keyword(s):  
Recent Work ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moore Space ◽  
Global Coherence ◽  
Topological Manifolds ◽  
Necessary And Sufficient ◽  
Moore Spaces ◽  
Significant Class

The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.

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