Probability theory

Denomination has been stabilized after the publication of RiskMetrics Technical Document in 1994, by JPMorgan. Note that the work accomplished by JPMorgan was more a pulic relation campaign than an advanced technical study : VaR is more a practice than a theory. “VaR summarizes the worst loss ever on a target horizon that will not be exceeded with a given level of confidence”, i.e. formaly it is a quantile of the projected distibution of gains and losses over the target horizon Till Guldimann (1992) created

of light simultaneously. Foundations In 1917, Albert Einstein established the theoretic foundations for the LASER and the MASER in the paper Zur Quantentheorie der Strahlung (On the Quantum Theory of Radiation); via a re-derivation of Max Planck’s law of radiation, conceptually based upon probability coefficients (Einstein coefficients) for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation; in 1928, Rudolf W. Ladenburg confirmed the existences of the phenomena

. . . . . . . . . . . 1.1 Probability foundations . . . . . . . . Basic set theory Disjointness Partition Sigma algebra Probability function Probability space Counting Conditional probability Bayes’ Rule Independence of events Mutual independence of events Random variables . . . . . . . . . . . Random variable Random vector Measurability Smallest σ-field Independence of r.v.s Independence of random vectors Mean independence Cumulative distribution function Probability mass function Marginal pmf Conditional

51e année, N. 4, 1996. pp. 873-905. Voir l'article en ligne An History of the Efficient Market Concept. WALTER. The so-called market efficiency, which states that prices fully reflect all available information is key concept of the modern financial theory. Actually, most of the practical mechanisms and financial instruments traded on markets are based on this hypothesis. This concept is closely related to probabilistic representation of the behavior of stock market prices. This representation allows

map 2.1 1. random sampling 2. descriptive statistics 3. large sample theory −→ convergence in probability −→ convergence in distribution −→ consistency × efficiency 4. point estimation −→ bias × variance −→ maximum likelihood × method of moments 5. hypothesis testing −→ holy trinity Random sampling 2.2 (x1, . . . , xn) is a random sample if the n observations correspond to independent draws from a single probability distribution function f (xi, θ ), where θ is a vector of unknown parameters

Werner (1987) ou Nielsen (1989)). Mentionnons ici cependant que l’adaptation de ces conditions générales semble particulièrement prometteuse pour ce qui concerne le sous-ensemble de NEURA correspondant au modèle “Expected Utility with Rank dependent Probability” (EURDP) proposé par Quggin (1982) et Allais (1988). Bien qu’étant un cas très particulier de préférences “non neumanniennes”, ce modèle d’expression simple et suffisamment général pour offrir une alternative crédible et féconde au modèle neumannien

method. Pascal was a mathematician of the first order. He helped create two major new areas of research. He wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646 he refuted Aristotle's followers who insisted that nature abhors a vacuum. His results caused many disputes before being

0033-295 X/89/S00.75 A Neural Theory of Binocular Rivalry Randolph Blake Northwestern University When the two eyes view discrepant monocular stimuli, stable single vision gives way to alternating periods of monocular dominance; this is the well-known but little understood phenomenon of binocular rivalry. This article develops a neural theory of binocular rivalry that treats the phenomenon as the default outcome when binocular correspondence cannot be established. The theory posits the existence of

assume that the growth rate of the endowment follows a Markov process. This is in contrast to the assumption in Lucas' model that the endowment leoel follows a Markov process. Our assumption, which requires an extension of competitive equilibrium theory, enables us to capture the non-stationarity in the consumption series associated with the large increase in per capita consumption that occurred in the 1889-1978 period. The economy we consider was judiciously selected so that the joint process governing

With the exception of initial forced bets, money is only placed into the pot voluntarily by a player who, at least in theory, rationally believes the bet has positive expected value. Thus, while the outcome of any particular hand significantly involves chance, the long-run expectations of the players are determined by their actions chosen based on probability, psychology and game theory. Poker has gained in popularity since the beginning of the 20th Century, and has gone from being primarily a recreational