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Ruin Theory
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin. Classical model The theoretical foundation of ruin theory, known as the Cramér–Lundberg model (or classical compound-Poisson risk model, classical risk process or Poisson risk process) was introduced in 1903 by the Swedish actuary Filip Lundberg. Lundberg's work was republished in the 1930s by Harald Cramér. The model describes an insurance company who experiences two opposing cash flows: incoming cash premiums and outgoing claims. Premiums arrive a constant rate ''c > 0'' from customers and claims arrive according to a Poisson process N_t with intensity \lambda and are independent and identically distributed non-negative random variables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuarial Science
Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, pension, finance, investment and other industries and professions. Actuary, Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis. Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, financial accounting and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory. Many universities have undergraduate and gradu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term ''convolution'' refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). Graphically, it expresses how the 'shape' of one function is modified by the other. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f*g differs from cross-correlation f \star g only in that either f(x) or g(x) is reflected about the y-axis in convolution; thus i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuarial Science
Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, pension, finance, investment and other industries and professions. Actuary, Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis. Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, financial accounting and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory. Many universities have undergraduate and gradu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chance-constrained Portfolio Selection
Chance-constrained portfolio selection is an approach to portfolio selection under loss aversion. The formulation assumes that (i) investor's preferences are representable by the expected utility of final wealth, and that (ii) they require that the probability of their final wealth falling below a survival or safety level must to be acceptably low. The chance-constrained portfolio problem is then to find: :Max \sum_wjE(Xj), subject to Pr(\sum_ wjXj < s) ≤ , wj = 1, wj ≥ 0 for all j, ::where s is the survival level and is the admissible probability of ruin; w is the weight and x is the value of the ''jth'' asset to be included in the portfolio. The original implementation is based on the seminal work of Abraham Charnes and [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Risk
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent. Modern portfolio theory initiated by Harry Markowitz in 1952 under his thesis titled "Portfolio Selection" is the discipline and study which pertains to managing market and financial risk. In modern portfolio theory, the variance (or standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...) of a portfolio is used as the definition of risk. Types According to Bender and Panz (2021), financial risks can be sorted into five different categories. In their study, they apply an algorith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans-Ulrich Gerber
Hans-Ulrich or Hans Ulrich is a German masculine given name. Notable people with the name include: * Hans Ulrich Aschenborn (born 1947), animal painter in Southern Africa * Hans-Ulrich Back (1896–1976), German general in the Wehrmacht during World War II * Hans-Ulrich Brunner (1943–2006), Swiss painter * Hans-Ulrich Buchholz (1944–2011), German rower * Hans-Ulrich Dürst (born 1939), Swiss former swimmer * Hans Ulrich von Eggenberg (1568–1634), Austrian statesman * Hans Ulrich Engelmann (1921–2011), German composer * Hans-Ulrich Ernst (1920–1984), known as Jimmy Ernst, American painter born in Germany * Hans Ulrich Fisch (1583–1647), Swiss painter * Hans Ulrich Franck (1590–1675), German historical painter and etcher from Kaufbeuren, Swabia * Hans-Ulrich Grapenthin (born 1943), German former footballer * Hans Ulrich Gumbrecht (born 1948), literary theorist whose work spans epistemologies of the everyday * Hans-Ulrich Indermaur (born 1939), Swiss television moderator, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elias S
Elias ( ; ) is the hellenized version for the name of Elijah (; ; , or ), a prophet in the Northern Kingdom of Israel in the 9th century BC, mentioned in several holy books. Due to Elias' role in the scriptures and to many later associated traditions, the name is used as a personal name in numerous languages. Variants * Éilias Irish * Elia Italian, English * Elias Norwegian * Elías Icelandic * Éliás Hungarian * Elías Spanish * Eliáš, Elijáš Czech * Elijah, Elia, Ilyas, Elias Indonesian * Elias, Eelis, Eljas Finnish * Elias Danish, German, Swedish * Elias Portuguese * Elias, Iliya () Persian * Elias, Elis Swedish * Elias, Elyas (ኤሊያስ) Ethiopian * Elias, Elyas Philippines * Eliasz Polish * Élie French * Elija Slovene * Elijah English, Hebrew * Elis Welsh * Elisedd Welsh * Eliya (එලියා) Sinhala * Eliyas (Ілияс) Kazakh * Eliyahu, Eliya (אֵלִיָּהוּ, אליה) Biblical Hebrew, Hebrew * Elyās, Ilyās, Eliya (, ) Arabic * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael R
Michael may refer to: People * Michael (given name), a given name * Michael (surname), including a list of people with the surname Michael Given name * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (fashion designer), Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian footballer Rulers Byzantine emperors *Michael I Rangabe (d. 844), married the daughter of Emperor Nikephoros I *Michael II (770–829), called "the Stammerer" and "the Amorian" *Michael III ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renewal Process
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponential distribution, exponentially distributed holding times, a renewal process may have any IID, independent and identically distributed (IID) holding times that have finite expectation. A renewal-reward process additionally has a random sequence of rewards incurred at each holding time, which are IID but need not be independent of the holding times. A renewal process has asymptotic properties analogous to the strong law of large numbers and central limit theorem. The renewal function m(t) (expected number of arrivals) and reward function g(t) (expected reward value) are of key importance in renewal theory. The renewal function satisfies a recursive integral equation, the renewal equation. The key renewal equation gives the limiting value of the convolution of m'(t) with a suitable non-negative function. The superposition of renewal processes can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M/G/1 Queue
In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated by a Poisson process), service times have a General distribution and there is a single server. The model name is written in Kendall's notation, and is an extension of the M/M/1 queue, where service times must be exponentially distributed. The classic application of the M/G/1 queue is to model performance of a fixed head hard disk. Model definition A queue represented by a M/G/1 queue is a stochastic process whose state space is the set , where the value corresponds to the number of customers in the queue, including any being served. Transitions from state ''i'' to ''i'' + 1 represent the arrival of a new customer: the times between such arrivals have an exponential distribution with parameter λ. Transitions from state ''i'' to ''i'' − 1 represent a customer who has been served, finishing being served ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Probability
Applied probability is the application of probability theory to statistical problems and other scientific and engineering domains. Scope Much research involving probability is done under the auspices of applied probability. However, while such research is motivated (to some degree) by applied problems, it is usually the mathematical aspects of the problems that are of most interest to researchers (as is typical of applied mathematics in general). Applied probabilists are particularly concerned with the application of stochastic processes, and probability more generally, to the natural, applied and social sciences, including biology, physics (including astronomy), chemistry, medicine, computer science and information technology, and economics. Another area of interest is in engineering: particularly in areas of uncertainty, risk management, probabilistic design, and Quality assurance. History Having initially been defined at a symposium of the American Mathematical Society in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
