Universal Laws and Economic Phenomena
This is a short commentary piece that discusses how the methods used in the natural sciences can apply to economics in general and financial markets specifically.
q-fin.GN↗
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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.
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Contrôle impulsionnel appliqué à la gestion de changement de technologie dans une entreprise
We consider an impulse control problem in infinite horizon applied with switching technology. We suppose that the firm decides at certain moments (impulse moments) to switch technology, leading to a jump of the firm value. We show that the value function for such problems satisfies a dynamic programming principle version. Our objective is to look for an optimal strategy which maximizes the value function associated with a switching problem.
math.PR↗
Regulation Simulation
A deterministic trading strategy by a representative investor on a single market asset, which generates complex and realistic returns with its first four moments similar to the empirical values of European stock indices, is used to simulate the effects of financial regulation that either pricks bubbles, props up crashes, or both. The results suggest that regulation makes the market process appear more Gaussian and less complex, with the difference more pronounced for more frequent intervention, though particular periods can be worse than the non-regulated version, and that pricking bubbles and propping up crashes are not symmetrical.
q-fin.GN↗
The Hazards of Propping Up: Bubbles and Chaos
In the current environment of financial distress, many governments are likely to soon become major holders of financial assets, but the policy debate focuses only on the likelihood and extent of short-term market stabilization. This paper shows that government intervention and propping up are likely to lead to long-term bubbles and even wildly chaotic behavior. The discontinuities occur when the committed capital reaches a critical amount that depends on just two parameters: the market impact of trading and the target exposure percentage.
q-fin.GN↗
Markets are efficient if and only if P = NP
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.
q-fin.GN↗
Arbitrage strategy
An arbitrage strategy allows a financial agent to make certain profit out of nothing, i.e., out of zero initial investment. This has to be disallowed on economic basis if the market is in equilibrium state, as opportunities for riskless profit would result in an instantaneous movement of prices of certain financial instruments. The principle of not allowing for arbitrage opportunities in financial markets has far-reaching consequences, most notably the option-pricing and hedging formulas in complete markets.
q-fin.GN↗
Free Lunch
The concept of absence of opportunities for free lunches is one of the pillars in the economic theory of financial markets. This natural assumption has proved very fruitful and has lead to great mathematical, as well as economical, insights in Quantitative Finance. Formulating rigorously the exact definition of absence of opportunities for riskless profit turned out to be a highly non-trivial fact that troubled mathematicians and economists for at least two decades. The purpose of this note is to give a quick (and, necessarily, incomplete) account of the recent work aimed at providing a simple and intuitive no-free-lunch assumption that would suffice in formulating a version of the celebrated Fundamental Theorem of Asset Pricing.
q-fin.GN↗
Is It Real, or Is It Randomized?: A Financial Turing Test
We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are challenged to distinguish actual financial market returns from random temporal permutations of those returns. We find overwhelming statistical evidence (p-values no greater than 0.5%) that subjects can consistently distinguish between the two types of time series, thereby refuting the widespread belief that financial markets "look random." A key feature of the experiment is that subjects are given immediate feedback regarding the validity of their choices, allowing them to learn and adapt. We suggest that such novel interfaces can harness human capabilities to process and extract information from financial data in ways that computers cannot.
q-fin.GN↗
Arbitrage Opportunities in Misspecified Stochastic volatility Models
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics is a classical Black-Scholes one, we give a new interpretation of the classical butterfly and risk reversal contracts in terms of their (near) optimality for arbitrage strategies. Our results are illustrated by a numerical example including transaction costs.
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Micro-Macro Relation of Production - The Double Scaling Law for Statistical Physics of Economy -
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the labor of one million Japanese firms. Theoretical study of the scaling laws suggests lognormal joint distributions of sales and labor and a scaling law for labor productivity, both of which are confirmed empirically. This framework offers characterization of the equilibrium distribution with a small number of scaling indices, which determine macroscopic quantities, thus setting the stage for an equivalence with statistical physics, bridging micro- and macro-economics.
q-fin.GN↗
The Problem of Modeling of Economic Dynamics (new version)
The correctness of Harrods model in the differential form is studied. The inadequacy of exponential growth of economy is shown; an alternative result is obtained. By example of Phillips model, an approach to correction of macroeconomic models (in terms of initial prerequisites) is generalized. A methodology based on balance relations for modelling of economic dynamics, including obtaining forecast estimates, is developed. The problems thus considered are reduced to the solution of Volterra and Fredholm integral equations of the second kind.
q-fin.GN↗
The Validity of Company Valuation Using Discounted Cash Flow Methods
This paper closely examines theoretical and practical aspects of the widely used discounted cash flows (DCF) valuation method. It assesses its potentials as well as several weaknesses. A special emphasize is being put on the valuation of companies using the DCF method. The paper finds that the discounted cash flow method is a powerful tool to analyze even complex situations. However, the DCF method is subject to massive assumption bias and even slight changes in the underlying assumptions of an analysis can drastically alter the valuation results. A practical example of these implications is given using a scenario analysis.
q-fin.GN↗
Overview of utility-based valuation
We review the utility-based valuation method for pricing derivative securities in incomplete markets. In particular, we review the practical approach to the utility-based pricing by the means of computing the first order expansion of marginal utility-based prices with respect to a small number of random endowments.
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Diagnosis and Prediction of Market Rebounds in Financial Markets
We introduce the concept of "negative bubbles" as the mirror image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a hazard rate describing the collective buying pressure of noise traders. The price fall occurring during a transient negative bubble can be interpreted as an effective random downpayment that rational agents accept to pay in the hope of profiting from the expected occurrence of a possible rally. We validate the model by showing that it has significant predictive power in identifying the times of major market rebounds. This result is obtained by using a general pattern recognition method which combines the information obtained at multiple times from a dynamical calibration of the JLS model. Error diagrams, Bayesian inference and trading strategies suggest that one can extract genuine information and obtain real skill from the calibration of negative bubbles with the JLS model. We conclude that negative bubbles are in general predictably associated with large rebounds or rallies, which are the mirror images of the crashes terminating standard bubbles.
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L'effet de levier de trésorerie
The effect of leverage on liquidity is a tool for analysing the level of liquidity for a given production process. It measures the sensitivity of the level of liquidity that results from changes in the volume of production and unit operating margin. A commercial activity is liquid at the moment when all costs are covered by revenues. However, not all of the cash flows from production influence liquidity levels. The estimated costs do not directly influence the level of liquidity. Therefore, two indicators are to be taken into consideration: the elasticity of ongoing liquidity - fixed costs include estimated costs, and, the elasticity of immediate liquidity - fixed costs only include costs that are payable. The coefficients of leverage of ongoing liquidity and of leverage of immediate liquidity in relation to the operating margin have a behaviour that is identical to that calculated in relation to production. If the productive capacity remains unchanged, the regulation of the change in elasticity of the costs and of its influence on the unitary operating margin is the sole parameter available to the entrepreneur to maintain the liquidity of the company at the desired level. But, if the productive capacity is variable, the entrepreneur can use the volume of sales to control liquidity but then the transformation of the production process must be analysed so as to adjust the relevant elements to retain in the operating structure the degree of liquidity wished for.
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Quantum Portfolios of Observables and the Risk Neutral Valuation Model
Quantum Portfolios of quantum algorithms encoded on qbits have recently been reported. In this paper a discussion of the continuous variables version of quantum portfolios is presented. A risk neutral valuation model for options dependent on the measured values of the observables, analogous to the traditional Black-Scholes valuation model, is obtained from the underlying stochastic equations. The quantum algorithms are here encoded on simple harmonic oscillator (SHO) states, and a Fokker-Planck equation for the Glauber P-representation is obtained as a starting point for the analysis. A discussion of the observation of the polarization of a portfolio of qbits is also obtained and the resultant Fokker-Planck equation is used to obtain the risk neutral valuation of the qbit polarization portfolio.
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Any Regulation of Risk Increases Risk
We show that any objective risk measurement algorithm mandated by central banks for regulated financial entities will result in more risk being taken on by those financial entities than would otherwise be the case. Furthermore, the risks taken on by the regulated financial entities are far more systemically concentrated than they would have been otherwise, making the entire financial system more fragile. This result leaves three directions for the future of financial regulation: continue regulating by enforcing risk measurement algorithms at the cost of occasional severe crises, regulate more severely and subjectively by fully nationalizing all financial entities, or abolish all central banking regulations including deposit insurance to let risk be determined by the entities themselves and, ultimately, by their depositors through voluntary market transactions rather than by the taxpayers through enforced government participation.
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Dynamic Bertrand Oligopoly
We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the dynamic setting. Within the static game, we characterize the Nash equilibrium when there are $N$ players with heterogeneous costs. In the dynamic game with uncertain market demand, firms of different sizes have different lifetime capacities which deplete over time according to the market demand for their good. We setup the nonzero-sum stochastic differential game and its associated system of HJB partial differential equations in the case of linear demand functions. We characterize certain qualitative features of the game using an asymptotic approximation in the limit of small competition. The equilibrium of the game is further studied using numerical solutions. We find that consumers benefit the most when a market is structured with many firms of the same relative size producing highly substitutable goods. However, a large degree of substitutability does not always lead to large drops in price, for example when two firms have a large difference in their size.
math.OC↗