Related papers: Elements for a Theory of Financial Risks
This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval {\Delta} results in…
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts…
The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…
The integration and innovation of finance and technology have gradually transformed the financial system into a complex one. Analyses of the causesd of abnormal fluctuations in the financial market to extract early warning indicators…
We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine theorem and L\'evian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an…
Aggregating risks from multiple sources can be complex and demanding, and decision makers usually adopt heuristics to simplify the evaluation process. This paper axiomatizes two closed related and yet different heuristics, narrow bracketing…
The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…
In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of…
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…
In this paper we extend the theory of option pricing to take into account and explain the empirical evidence for asset prices such as non-Gaussian returns, long-range dependence, volatility clustering, non-Gaussian copula dependence, as…
We show how importance sampling can be used to reconstruct the statistics of rare cosmological fluctuations in stochastic inflation. We have developed a publicly available package, PyFPT, that solves the first-passage time problem of…
Throughout history, many countries have repeatedly experienced large swings in asset prices, which are usually accompanied by large fluctuations in macroeconomic activity. One of the characteristics of the period before major economic…
In competitive industries, a reliable yield forecasting is a prime factor to accurately determine the production costs and therefore ensure profitability. Indeed, quantifying the risks long before the effective manufacturing process enables…
In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus which is an…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
In this paper we discuss a scaling approach to business fluctuations. Our starting point consists in recognizing that concepts and methods derived from physics have allowed economists to (re)discover a set of stylized facts which have to be…