No-Arbitrage Principle in Conic Finance

A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time

The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions

We now return to general continuous-time financial market models in the setting of §6.1, i.e. there are d+1 primary traded assets whose price processes are given by stochastic processes S 0,... , S d , which are assumed to be adapted, right-continuous with left-limits (RCLL) and strictly positive semimartin-gales on a filtered probability space (Ω, F ℙ, F) (as usual F = (F t ) t≤T ). We assume that the market is free of arbitrage, in the sense that there exist equivalent martingale measures, but it contains non-attainable contingent claims, i.e. there are cash flows which cannot be replicated by self-financing trading strategies. In view of Theorem 6.1.5 this means that we do not have a unique equivalent martingale measures. We try to answer the obvious questions in this setting: how should we price the non-attainable contingent claims, i.e. which of the possible equivalent martingale measures should we pick for our valuation formula based on expectation, and, how can we construct hedging strategies for the nonattainable contingent claims to ‘minimise the risk? We try to answer these two questions in the general setting and then consider a prominent example of an incomplete market, a market with stochastic volatility, in more detail.KeywordsTrading StrategyStochastic VolatilityContingent ClaimMartingale MeasureIncomplete MarketThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This book provides a basic grounding in the use of probability to model random financial phenomena of uncertainty, and is targeted at an advanced undergraduate and graduate level. It should appeal to finance students looking for a firm theoretical guide to the deep end of derivatives and investments. Bankers and finance professionals in the fields of investments, derivatives, and risk management should also find the book useful in bringing probability and finance together. The book contains applications of both discrete time theory and continuous time mathematics, and is extensive in scope. Distribution theory, conditional probability, and conditional expectation are covered comprehensively, and applications to modeling state space securities under market equilibrium are made. Martingale is studied, leading to consideration of equivalent martingale measures, fundamental theorems of asset pricing, change of numeraire and discounting, risk-adjusted and forward-neutral measures, minimal and maximal prices of contingent claims, Markovian models, and the existence of martingale measures preserving the Markov property. Discrete stochastic calculus and multiperiod models leading to no-arbitrage pricing of contingent claims are also to be found in this book, as well as the theory of Markov Chains and appropriate applications in credit modeling. Measure-theoretic probability, moments, characteristic functions, inequalities, and central limit theorems are examined. The theory of risk aversion and utility, and ideas of risk premia are considered. Other application topics include optimal consumption and investment problems and interest rate theory.

In a continuous time market model we consider the problem of existence of an equivalent martingale measure with density lying within given lower and upper bounds and we characterize a necessary and sufficient condition for this. In this sense our main result can be regarded as a version of the fundamental theorem of asset pricing. In our approach we suggest an axiomatic description of prices on Lp-spaces (with p ∈[1, ∞)) and we rely on extension theorems for operators.

Arbitrage, Hedging and Utility Maximization Using Semi-Static Trading Strategies with American Options

We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no‐arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs. We consider a market with a single risky asset whose ask price process is higher than or equal to its bid price process. Neither the concatenation property of the set of wealth processes, that is used in the proof of the frictionless FTAP, nor some boundedness property of the trading volume of admissible strategies usually argued within models with a nonvanishing bid–ask spread need to be satisfied in our model.

We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.

We show that the absence of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values within the bid-ask intervals that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska’s classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs.

Some Examples of the Role of Finance in Enabling Mathematics

In order to comprehend the U.S. Private equity's influence on nursing facilities, financial modeling is a good metric to assess facilities' financial health and fundamentals. To achieve this, I utilize Discounted Cash Flow Models (DCF) and Leveraged Buyout Models (LBO), along with various financial valuation models. The financial fundamentals, market trends, and market sentiments of companies can indicate their operational and financial sustainability. The objective of this project is to gain insights into how different valuation models and methods can forecast a company's financial health before and after the private equity (PE) acquisition. The outcomes of this project demonstrate a correlation between financial modeling and fundamental analysis in analyzing skilled nursing facilities and their relationship with Private Equity sponsors. These results were obtained through the implementation of financial valuation models to make predictions. The financial data parameters were analyzed using a genetic financial modeling method, considering factors such as revenue, expenses, net operating income, earnings before interest, taxes, depreciation, and amortization (EBITDA), enterprise value, etc. Results were obtained after an extensive optimization and analysis process, involving approximately 200,000 data points, conducted over a dura-tion of 200 hours.

Statistical arbitrage with default and collateral

This paper provides a theoretical analysis on the impacts of using a suboptimal information set for the estimation of the pricing kernel and, more in general, for the validity of the fundamental theorems of asset pricing. While inferring the risk-neutral measure from options data provides a naturally forward-looking estimate, extracting the real world measure from historical returns is only partially informative, thus suboptimal with respect to investors’ future beliefs. As a consequence of this disalignment, the two measures no longer share the same nullset, thus distorting the investors’ risk premium and the validity of the pricing measure. From a probabilistic viewpoint, the missing beliefs are totally unaccessible stopping times on the coarser filtration set, so that an absolutely continuous strict local martingale, once projected on it, becomes continuous with jumps. Some empirical examples complete the paper.

The purpose of this study was to establish the impact of discount rates on cut-off grades for narrow tabular gold deposits as characterized by the goldfields of the Witwatersrand Basin in South Africa. There are various methods available for determining the cut-off grade, from simple breakeven calculations to sophisticated software packages that consider a variety of inputs to optimize the cut-off grade. For this study a simple financial model was created in Microsoft Excel ® that links the ore flow, block listing, and the cash flow. This allows the cut-off grade to be optimized considering how the cost of capital and chosen discount rate affect the cash flow. The discounted cash flow (DCF) and resultant net present value (NPV) are a widely used valuation method for production properties according to the South African Code for the Reporting of Mineral Asset Valuation (SAMVAL Code). The financial model in this study utilizes the Solver function, as well as simple Microsoft Excel spreadsheet formulae to optimize the NPV. Solver was chosen as it is a standard feature in Excel and thus no additional software costs are incurred beyond the basic Microsoft Office suite. For the purpose of this study, just narrow tabular gold deposits of the Witwatersrand Basin were considered. An example of a typical ore block listing, as well as the costing figures, was obtained from an operating gold mine. The results obtained from the study financial model were compared to the current cut-off grades obtained from the mine using their proprietary optimizer program, and were found to be comparable. The methodology utilized for this study thus appears valid. The cut-off grade was optimized considering the cash flow, which includes the variable mineral resource royalty tax, the variable gold income tax, as well as the discount rate. By comparing the resultant NPVs using discount rates of zero, 9%, and 12%, the impact of the discount rate on cut-off grades, resultant life of mine, and average mining grades (AMG) could be compared for the example ore block listing.

Summary. The article proposes a financial model for a motor vehicle service enterprise and provides examples of its application. Research object: the operational process of a motor vehicle service enterprise. Purpose of the article: to develop an adapted financial model for motor vehicle service enterprises, enabling the assessment of startup prospects, strategic planning, and business development. The authors propose a comprehensive approach that considers revenues, expenses, cash flows, and investment attractiveness. Research methods: mathematical modeling of processes. The proposed financial model enables the evaluation of the feasibility of investment projects for establishing a motor vehicle service enterprise or improving specific aspects of its operations. Using the model, economic efficiency indicators that do not consider the time factor can be assessed, including: profit margin, payback period of initial investments, project profitability, as well as indicators for projects requiring a significant time frame. In such cases, time-sensitive indicators are used, such as net present value (NPV), discounted payback period, and internal rate of return (IRR). Calculations of some of these indicators are provided earlier in the article. Key aspects of the financial model: 1) forecasting revenues and expenses: estimation of the annual production program, labor intensity, revenues, and expenses to justify economic feasibility; 2) efficiency analysis: the methodology includes calculating indicators such as net profit, profitability, break-even point, and project payback period; 3) risk assessment: applying sensitivity analysis to identify key factors affecting profitability. Results: 1) the model allows for analyzing projects with varying levels of risk and incorporates the time factor; 2) the model facilitates the determination of economic efficiency using indicators such as net present value (NPV), internal rate of return (IRR), as well as indicators that do not account for discount rates. Practical significance: the research results are of practical value for auto service enterprises. Forecasting based on the model helps substantiate investments, optimize costs, and ensure business stability. Research prospects: further studies aim to enhance the model, develop methods for risk assessment, and improve forecasting depending on changes in economic conditions. Key conclusions: 1) the financial model is an effective tool for managerial decision-making; 2) the integration of economic efficiency evaluation methods reduces investment risks and optimizes the activities of auto service enterprises. Keywords: motor vehicle service enterprise, financial model, revenue, expenses, profit, efficiency, margin, payback period, net present value, risks, break-even point.