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Proebsting's Paradox
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008.E. O. Thorp, Understanding the Kelly Criterion: Part II, Wilmott Magazine, September 2008 The paradox was named for Todd Proebsting, its creator. Statement of the paradox If a bet is equally likely to win or lose, and pays b times the stake for a win, the Kelly bet is: : f^ = \frac \! times wealth.J. L. Kelly, Jr, A New Interpretation of Information Rate, Bell System Technical Journal, 35, (1956), 917–926 For example, if a 50/50 bet pays 2 to 1, Kelly says to bet 25% of wealth. If a 50/50 bet pays 5 to 1, Kelly says to bet 40% of wealth. Now suppose a gambler is offered 2 to 1 payout and bets 25%. What should he do if the payout on new bets cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelly Criterion
In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. John Larry Kelly, Jr, J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956. Because the Kelly Criterion leads to higher wealth than any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity), it is a scientific gambling method. The practical use of the formula has been demonstrated for gambling and the same idea was used to explain Diversification (finance), diversification in investment management., page 184f. In the 2000s, Kelly-style analysis became a part of mainstream investment theory and the claim has been made that well-known successful investors incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward O
Edward is an English given name A given name (also known as a forename or first name) is the part of a personal name quoted in that identifies a person, potentially with a middle name as well, and differentiates that person from the other members of a group (typically a fa .... It is derived from the Anglo-Saxon name ''Ēadweard'', composed of the elements '' ēad'' "wealth, fortune; prosperous" and ''wikt:weard#Old English, weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the House of Normandy, Norman and House of Plantagenet, Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III of England, Henry III named his firstborn son, the future Edward I of England, Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Todd Proebsting
Todd or Todds may refer to: Places ;Australia: * Todd River, an ephemeral river ;United States: * Todd Valley, California, also known as Todd, an unincorporated community * Todd, Missouri, a ghost town * Todd, North Carolina, an unincorporated community * Todd County, Kentucky * Todd County, Minnesota * Todd County, South Dakota * Todd Fork, a river in Ohio * Todd Township, Minnesota * Todd Township, Fulton County, Pennsylvania * Todd Township, Huntingdon County, Pennsylvania * Todds, Ohio, an unincorporated community People * Todd (given name) * Todd (surname) Arts and entertainment * ''Todd'' (album), a 1974 album by Todd Rundgren * Todd (''Cars''), a character in ''Cars'' * Todd (''Stargate''), a recurring character in the series ''Stargate Atlantis'' * The Todd (''Scrubs''), a character on ''Scrubs'' Other uses * Todd (elm cultivar) * Todd class, a characteristic class in algebraic topology * Todd-AO, a company in film post-production * Todd Corporation, a New Zeal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds
Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. Odds also have a simple relation with probability: the odds of an outcome are the ratio of the probability that the outcome occurs to the probability that the outcome does not occur. In mathematical terms, where p is the probability of the outcome: :\text = \frac where 1-p is the probability that the outcome does not occur. Odds can be demonstrated by examining rolling a six-sided die. The odds of rolling a 6 is 1:5. This is because there is 1 event (rolling a 6) that produces the specified outcome of "rolling a 6", and 5 events that do not (rolling a 1,2,3,4 or 5). The odds of rolling either a 5 or 6 is 2:4. This is because there are 2 events (rolling a 5 or 6) that produce the specified outcome of "rolling either a 5 or 6", and 4 events that do n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aaron Brown (financial Author)
Aaron C. Brown (born November 27, 1956) is an American finance practitioner, well known as an authorStephen Schurr, , Financial Times, March 20, 2006 on risk management and gambling-related issues. He also speaks frequently at professional and academic conferences. He was Chief Risk Manager at AQR Capital Management. He was one of the original developers of |
Gambling Mathematics
Experiments, events and probability spaces The technical processes of a game stand for experiments that generate aleatory events. Here are a few examples: * Throwing the dice in craps is an experiment that generates events such as occurrences of certain numbers on the dice, obtaining a certain sum of the shown numbers, and obtaining numbers with certain properties (less than a specific number, higher than a specific number, even, uneven, and so on). The sample space of such an experiment is for rolling one die or for rolling two dice. The latter is a set of ordered pairs and counts 6 x 6 = 36 elements. The events can be identified with sets, namely parts of the sample space. For example, the event ''occurrence of an even number'' is represented by the following set in the experiment of rolling one die: . * Spinning the roulette wheel is an experiment whose generated events could be the occurrence of a certain number, of a certain color or a certain property of the numbers (low, high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Paradoxes
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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