Nikolay Suchacev — PhD, St. Albina Girfanova, PhD — St. Petersburg, the Russian FederationProf. Laszlo Borbas. Engineer Dan C. The coming out of the risk concept is identified withthe coming into being of the probabilities theories the mathematic theory of probabilities. For the analysis developed in this work, we shall see that the yields thepercentage or logarithmic modifications of the assets price are considered in the riskmanagement as being stochastic variables.
The distribution of these yields is studied byboth academicians and market operators. More distributions have been identified as beingpossible distributions starting with the normal distribution or logo normal used by BlackScholes and Merton.
There is no demonstration of the fact that the yields distribution is notto be found, which keeps on leaving place to further developments of more and morecomplex functions of distribution.
Pascal and Pierre de Fermat have deepened the mathematical analysis of thegambles, which led to the consecration of a new branch of mathematics. Afterin lessthan 50 years, the classical instruments for measuring the risk came out.
The first one wasthe statistical sample, an application of the probabilities covering a vast range of issues —from those of juridical nature up to mechanics problems. This method has graduallyinvolved new developments of the insurances sector, such as the one covering the lifeexpectation. The result of transposing these data in form of graphs depending on thefrequency of occurrence a graph having on the ordinate the height of some individuals,and the occurrence frequency on the abscise has been named distribution or repartition.
In recognition of its significance, it was called normal distribution repartition. The most interesting discovery as regards the normal distribution is the factthat the nature itself contains something aleatory which can be characterized by thisrepartition.
by members of
For the mathematicians this fact became a very important instrument — thenormal distribution explains what is aleatory in nature and can be described by twomeasures only — the mean and the dispertion.
The normal distribution has the property of being asymmetrical as against themean, while the dispersion measures the width of the central curve of the bell.
Beyond thiscentral curve the normal distribution is extending and tends towards zero. Another feature of interest for the subsequent theoretical developments of thework consists of the fact that, in the case there is a number big enough of the doneobservations, all these observations being aleatory variables, independent two by two andhaving the same repartition and non-null dispersions, then the final repartition of all theseobservations tends to the normal one.
This property is known as the Central Limit Theorem.
The search of the general conditions so that the repartition of a sum of aleatoryindependent variables tends towards a normal repartition by increasing the terms number,led to the development of another direction in the theory of the limit theorems for sums ofaleatory independent variables, very closely connected with the stochastic processes.
Theproblems to face in this respect were of the following kind: what repartitions besides thenormal one may be linear repartitions of certain sums of aleatory variables? The conclusionbeing reached is that only the normal repartition is a repartition limit 1. Utility and the principle of the decreasing marginal utilityThe hypothesis of the expected utility is a result of the solution given by DanielBernoulli in to the famous paradox St. Petersburg enounced in by NicholasBernoulli.
The development is grounded by the principle of the representation of theconsumption plans from the perspective of the expected utility expected value - E vasaverage of the possible values as a result of the choice of an action direction, weighted withthe probabilities of coming out of these values25 and is considered a good evaluation of theaverage gains or losses which we can record within a long series of experiences 1.
Bernoulli proposed the following game St. If B hits the escutcheon for the first time with the second throwing, A pays him22 ducats and so on, the bank doubling the steak as many times hitting the escutcheon isdelayed by another throwing. If B hits the escutcheon for the first time by the n-ththrowing, review anti aging ristra gains 2n ducats.
The paradox is that the amount that can be gained is infinite. The mathematic expectation of B can explain this thing. The probability that the escutcheonappears after the first throwing is of VS. The probability that the mark appears from thefirst throwing and the head appears by the second throwing will be The gain, if the coming out of the escutcheoncoming out is delayed up to the n-th throwing counts for review anti aging ristra ducats.
However, while the expected gain isinfinite, we cannot presume, at least intuitively, that somebody will want to pay an infiniteamount in order to enter this game. The solution of Daniel Bernoulli was based on twoideas that have been considered as important by the economists of the XX century.
First of all, he maintains that the value which a person gives to a risky asset is notthe same with the expected gain of this one but, merely, with the expected utility of it — theimportance given presently by a certain person for obtaining the respective amount.
On theother hand, Bernoulli maintains that the utility that people grant to a gainu vis notlinearly dependent on the gain vbut increases with a rate which gets reduced — theprinciple of the decreasing marginal utility by adding a dollar to a fortune of 5 dollars maymean a significant increase but means lesser and lesser to the extent the wealth is larger. Bernoulli suspected that the expected utility of the game St.
Petersburg is finite if theutilities decrease to the extent the amount increases. Consequently, it will desirable to review anti aging ristra afinite amount of money in order to enter this game, even if the expected gain is infinite. Von Neumann and Morgenstern take over this idea in order to build up a system ofcalculation of the equilibrium under the conditions when people are adverse to risk.
Theprinciple of the decreasing marginal utility is one of the pillars of the theory of the assetsevaluation under conditions of uncertainty.
A significant element for the risk analysis is thetendency to the mean, discovered by Francis Galton. The regression at mean expresses thefact that, on long term basis, all the individuals tend towards an average value — in time,the extremes tend to approach the mean. The experiences achieved by Galton by the end ofthe XlX century have demonstrate the existence of this phenomenon in the heredity domainand set up this truth as being generally valid as universal statistical rule.
Those who studiedthe outcomes obtained by Galton have noticed the general applicability in many domains,mainly review anti aging ristra meteorology, the equities market, the accidents frequency and the economiccycles΄ domain. For our analysis, this discovery is important from the angle of the statisticalestimations of the coefficients of causality΄ relations or of connection between two aleatoryvariables.
The identification in probabilistic terms of the parameters of an equation showingus the relation between two or more aleatory variables has been called regression in order toreflect the regression phenomenon submitted above.
A model of the risk managementTo put in practice the relevant theories meant to obtain a measurement unit of therisk requires the construction of mathematical models and their testing in order to establishthe best methods or principles that may apply.
We shall analyze further on, the significanceand the main arguments regarding the utilization of a mathematical model and, afterwards,we shall approach the most frequently used methods in order to create review anti aging ristra. A mathematical model is a simplified mathematical representation of a system,process or theory of the real world with the purpose to understand, anticipate or evencontrol their behavior.
The utilization of the mathematical instruments with the purpose of analyzingthe economic processes led to the creation of a number of econometric models thatborrowed concepts from mechanics. Frisch referred to the Econometrics Society that cameout as a result of the consolidation of communities of economists- review anti aging ristra and thatwas supposed to gain more and more terrain during the coming years.
These propensitiestowards models with mechanical character, borrowed from physics, have been frequentlyfought with. From all the great theoreticians in economics, a percentagehigh enough were acquainted with at least a small training in mathematics. A model for the risk measurement is aiming to find out a relation that allows acertain drawing of the future fluctuations of the portfolio value. Most of the times this canbe obtained by the achievement of certain predictions regarding the changes taking place atthe level of the price for each instrument composing the analyzed portfolio, based on thehistory of these instruments prices only.
This entire construction implies the modeling oftwo components: the temporally dynamics of the yields, namely the modeling of theevolution in time of these yields; and the yields distribution at a certain moment. The necessity of the risk managementStrictly academically, the companies seem to pay an interest somehow curious forthe risk administration and management.
Thisis the reason for the act that the exposure to the specific risk will be not rewarded by themarket. The investing agents are forming their portfolios composed by the risk-free assetalong with a mix of risky assets, while the weights relating to the two categories of equitiesare set up depending on the investors΄ aversion to risk.
According to Modigliani — Millertheorem which is also known as the theorem of the irrelevance of the capital structure ,the value of a company is independent of the risk structure.
Thus, the companies shouldmaximize the expected profits, irrespectively the risk they are exposed to, taking intoaccount the fact that the shareholders might eliminate the risk by diversification. Nevertheless, the economists Modigliani and Miller showed the reasons that are notallowing this theory to be validated in practice.
The risk management acquired a significantimportance this being due to the imperfections of the capital market, such as the taxes andthe bankruptcy costs. The present market value of a company will be diminishedby the costs concerning the reorganizing process or, in most severe circumstances, by theactivity cease.
This is a reason for review anti aging ristra management may increase the value of the companyby means of reducing the bankruptcy review anti aging ristra. Numerous systems of taxation contain various modalities of carryingforward the taxation advantages for the past losses if, ceteris paribus, the diminishing of thevolatility of the future gains will lead to the decrease of the up-dated value review anti aging ristra all the futurepayments and will generate the increase of the company΄ s value.
One of the biggest sources of bankruptcy is givenby the incapacity of the companies to honor its debts. Therefore, to the extent the degree ofrunning into debt of review anti aging ristra company is higher, its risk will be higher. The appropriatemanagement of the risk review anti aging ristra maintain a high level of running into debt rates allowing thus amore aggressive extension of the company, as much as this financing source is notexpensive. By participating to theactivity of the company, its employees have themselves an implicit exposure to the risksthat the company they work for is facing.
Anghelache, G. Lintner, J. Mossin, J. Singer, B. Sharpe, W. Treynor, J. For an actual analyse of phenomena development over time, it use as studyinstrument the statistical adjustment series, the purpose of ascertaining them in last periodand, by extrapolation to predict future developments. Key words: variability, dinamic series, interdependence, relative indicator,growth rateJEL Classification: C22Some general aspectsThe chronological series composed of two rows of parallel data, the first rowsshow variation of the time periods variation and the second rows show the variation of thephenomenon or characteristics studied over time.
The chronological series has thefollowing features: variability, homogenity, interdependence to its terms. The variability isbecause each term is obtained by centralizing of cel mai bun anti-îmbătrânire facial nyc data different as level ofdevelopment.
These individual data exist because, that in social phenomena acts besides theessential causes, determinants causes, and a sufficient number of nonessential causes.
When analyzing time series, we have to take into account the fact that they are prepared forthe complex units. For them, the degree of variation of indicators includes structuralvariations from one time unit to another.
(National Institute of Economic Research, Romanian Academy)
Interdependent of terms: the indicators are successive values of the somephenomena recorded in the some teritorial or administrative forfait fiscaux suisse anti aging. In time series need toknow the trend curve specific to each stage of development, and statistical expressing is theaction of the low even causing them.
Taking into account all these particularities, thestatistical analysis of chronological series shall be based on a system of indicators thatcharacterize many quantitative relations of the inside of series and at the period to whichdata is referring. The absolute indicators of the time series are expressed in the units ofmeasurement of the phenomenon under study.
In this paper we uses :y 0y Absolute increase or decrease is calculated from the level of a single periodconsidered as base of reference or from a period of time to another. In the first case, weobtain absolute increase or decrease calculated with fixed base, in the second case weobtain absolute increase or decrease calculated with the chained base known as absoluteincrease or decrease with variable base 1.
In the time series with y i terms i 0 n we obtain n absolute increase. The relative indicators of the time series are very important for analyzing thedynamic of the socio-economic phenomena. These indicatos are used frequently to determine the proportions and corellationsbetween the various branches and sectors of the national economyRelative size showinghow many times a phenomenon over time has changed is called dynamic index and it canbe calculated with fixed base and variable base.
Calculation of absolute and relative indicators conduct to the review anti aging ristra ofindividual relationships between the terms of a series, taken by two.
These indicators shows the variability of the terms of noua îngrijire a pielii anti-îmbătrânire pentru frumusețe time series as a result ofthe influence of all causes and conditions that determine the evolution of this phenomenon. When analyzing dynamics of phenomena can calculate the average level andaverage rate.
You’re Temporarily Blocked
The average of the time series. If we represent on an axis the terms of a chronological series of intervals, they willappear as:y 0 y 1 y 2 y 3. The average of the time series of interval be calculed using simple arithmeticaverage :ni0yiy. If in the inside of the same series can be found opposite trends, that on review anti aging ristra graph,corresponding to a change in the form of a second degree parabola with a maximum orminimum point, then the series should be divided into two parts, calculating the respectiveaverage indicators.
The average growth rata shows how much this phenomenon has increased in sizerelative,in the analyzed period, on average from one unit to another of interval. The average growth rata is calculated as the difference between dynamicenvironment index, expressed as a percentage.