Related papers: Theory of Financial Risk: Basic notions in probabi…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In…
This paper introduces a novel approach to financial crisis prediction by establishing a thermodynamic-like framework derived from the fluctuation theorem of statistical physics. We define market temperature through the probability ratio of…
The purpose of this article is to propose a new "theory," the Strategic Analysis of Financial Markets (SAFM) theory, that explains the operation of financial markets using the analytical perspective of an enlightened gambler. The gambler…
Plotting a learner's average performance against the number of training samples results in a learning curve. Studying such curves on one or more data sets is a way to get to a better understanding of the generalization properties of this…
A financial market is a system resulting from the complex interaction between participants in a closed economy. We propose a minimal microscopic model of the financial market economy based on the real economy's symmetry constraint and…
Given the constant rise in quantity and quality of data obtained from neural systems on many scales ranging from molecular to systems', information-theoretic analyses became increasingly necessary during the past few decades in the…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
There are various metrics for financial risk, such as value at risk (VaR), expected shortfall, expected/unexpected loss, etc. When estimating these metrics, it was very common to assume Gaussian distribution for the asset returns, which may…
We generalize the momentum indicator idea taking into account the volume of transactions as a multiplicative factor. We compare returns obtained following strategies based on the classical or the generalized technical analysis, taking into…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused…
In this paper we state the fundamental principles of the gauge approach to financial economics and demonstrate the ways of its application. In particular, modelling of realistic price processes is considered for an example of S&P500 market…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect…