J. Kelly. A new interpretation of information rate. Bell Systems Technical Journal, 35:917-926, 1956.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the maximum entropy of the predictability of X and bounded below by the segmented self information of the predictability of X, and that these bounds are tight. 1 Introduction The relationship between prediction and gambling has been investigated for decades. In the 1950s, Shannon [21] and Kelly [10] studied prediction and gambling, respectively, as alternative means of characterizing information. In the 1960s, Kolmogorov [11] and Loveland [12] introduced a strong notion of unpredictability of in nite binary sequences, now known as Kolmogorov Loveland stocasticity. In the early 1970s, Schnorr ....

J. Kelly. A new interpretation of information rate. Bell Systems Technical Journal, 35:917-926, 1956. Prediction and Dimension 17

....our model of a stationary ergodic process. They show that the fault rate of a Ziv Lempel [27] based prefetching algorithm approaches the fault rate of the best prefetcher (which has full knowledge of the Markov source) for the given Markov source as the page request sequence length n 1. Kelly [19] was the rst to study the relation between data compression, entropy and gambling, showing that the outcome of a horse race gambling with fair odds is fully characterized by the entropy of the stochastic process. It was shown [19, 2] that the growth rate of investment in the horse race is equal ....

....Markov source as the page request sequence length n 1. Kelly [19] was the rst to study the relation between data compression, entropy and gambling, showing that the outcome of a horse race gambling with fair odds is fully characterized by the entropy of the stochastic process. It was shown [19, 2] that the growth rate of investment in the horse race is equal to log m H , where m is the number of horses and H is the entropy of the source. 1 An online algorithm ALG has a competitive ratio of c if there is a constant such that for all nite input sequences I, ALG(I) c OPT(I) where ....

J. Kelly, A New Interpretation of Information Rate, Bell Sys. Tech. Journal, 35, 1956, 917-926.

....our model of a stationary ergodic process. They show that the fault rate of a ZivLempel [28] based prefetching algorithm approaches the fault rate of the best prefetcher (which has full knowledge of the Markov source) for the given Markov source as the page request sequence length n 1. Kelly [19] was the rst to study the relation between data compression, entropy and gambling, showing that the outcome of a horse race gambling with fair odds is fully characterized by the entropy of the stochastic process. It was shown [19, 2] that the growth rate of investment in the horse race is equal ....

....Markov source as the page request sequence length n 1. Kelly [19] was the rst to study the relation between data compression, entropy and gambling, showing that the outcome of a horse race gambling with fair odds is fully characterized by the entropy of the stochastic process. It was shown [19, 2] that the growth rate of investment in the horse race is equal to log m H, where m is the number of horses and H is the entropy of the source. Similar results have been shown for portfolio selection strategies in equity market investments [3, 6] Our results on list accessing are based on the work ....

J. Kelly, A New Interpretation of Information Rate, Bell Sys. Tech. Journal, 35, 1956, 917-926.

....the standard assumption needed to ensure the existence of an equivalent martingale measure. We will not use expected utility maximization, equilibrium arguments or an equivalent martingale measure. Instead, we start from the concept of a growth optimal portfolio #GOP#, originally developed by Kelly #1956# and further developed in a stream of literature leading to Long #1990#, Artzner #1997#, Bajeux Besnainou Portait #1997#, Karatzas Shreve #1998#, Platen #2000# and Heath Platen #2001#. The GOP is also known as the numeraire portfolio and appears in the APT as the inverse state price ....

....#t# 2 #2.17# for t 2 #0;T#. Wenowchoose in our multi asset market a self #nancing benchmark portfolio. In particular, we construct it to be such that its long term growth cannot be outperformed byany other portfolio. This portfolio is known as growth optimal portfolio #GOP#, discovered by Kelly #1956#. It achieves the maximum domestic growth rate at each time t 2 #0;T#. In the following, we denote a self #nancing strategy that generates such a GOP by # = f##t# = ## 0 #t#; # d #t## # , t 2 #0;T#g. A necessary condition for achieving the maximum domestic growth rate by a ....

Kelly, J. R. #1956#. A new interpretation of information rate. Bell Syst. Techn.

....and later, with several remarkable confirmations. A June 1998 New York Times Science Times article attributed the degrees of separation idea to a sociologist in 1967. Yet it was well known to Shannon in 1960. For bet sizing in favorable games, Shannon suggested I look at a 1956 paper by Kelly [3]. I did and adapted it as our guide for blackjack and roulette, and used it later in other favorable games, sports betting, and the stock market [9, 13] The principle was to bet to maximize the expected value of the logarithm of wealth. This has desirable properties that are discussed in detail ....

J.L. Kelly, "A New Interpretation of Information Rate," Bell System Technical Journal, Vol. 35, 1956, pp. 917-926.

.... Having detailed the trading model, the specifications for the optimal fixed fraction trading, or Optimal f , calculations are adapted below per the method provided in Vince (1990) The basic approach proposed by Vince is an adaptation of an engineering solution to data transmission modelling by Kelly (1956, in Vince, 1990) Vince s (1990) research attempts to identify how many contracts should be traded for a portfolio dollar value, including the allowance for reinvestment of profits. The analysis relies on the determination of the optimal number of futures contracts to be taken per buy sell ....

Kelly, J.L. Jnr (1956), "A New Interpretation of Information Rate", Bell Systems Technical Journal, pp 917-926, July, 1956.

.... t X ; where the maximum is over all portfolio choices b : V B. Here V denotes the alphabet for V and B is the (m Gamma 1) dimensional probability simplex, B = fb 2 R m : b i 0; m X i=1 b i = 1g: The idea of maximizing growth rate of wealth in the stock market was introduced by Kelly [20]. In the general market, no closed form for the optimum portfolio b or the optimum doubling rate W exists. Barron and Cover [8] showed that, in the presence of side information V , the increase in the doubling rate DeltaW is bounded above by I(X; V ) In this work, we consider a slightly ....

....m X i=1 p i log o i : Note that D(pkb) is minimized (and is equal to 0) when b = p. Therefore, the optimum portfolio is b i = p i ; for i = 1; m: The optimum strategy for the gambler is to bet in proportion to the underlying probability distribution. This was established by Kelly [20]. Proportional gambling CHAPTER 3. HORSE RACE MARKET 17 is also known as Kelly gambling. The optimum doubling rate W is then given by W (X) m X i=1 p i log o i Gamma H(X) 3.2) Now suppose the gambler has side information Y about the outcome of the race. We assume that X and Y ....

J. Kelly. A new interpretation of information rate. The Bell System Technical Journal, 35:917--926, 1956.

....the different actions available and pick the sequence of actions that leads to the highest expected payoff. Since we make playing decisions that are independent of the bet size, these depend only on our hand, the state of the deck and the dealer s exposed card. This problem has been studied by others since 1956 when Baldwin et al. 1] determined the optimal strategy for games played with a full deck and only one hand of play per deck. In contrast, in this paper we focus on optimal betting for whatever playing strategy is chosen optimal or otherwise. Although our results may be of interest to ....

....count is kept by adding the value of every card seen. A true count converts this count by the size of the remaining deck. Desirable point count systems are highly correlated with the expected outcome of each hand. 4 One optimal betting scheme for Bernoulli games is the Kelly criterion [14] that maximizes the exponential rate of growth. If a player knows he has a 2 advantage (e.g. from an approximation based on a point count) he bets 2 of his bankroll. Although the assumptions don t apply to blackjack, many blackjack books recommend it be used to determine bet sizes. There have ....

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Kelly, J. L., 1956, A new interpretation of Information Rate. The Bell System Journal, July, pp. 917-926.

....application were driven by HTML, VBScript, JavaScript, or Java Applets, the approach would be similar, so there would be no need to adjust the agent even if the merchant went to XML and stylesheets for example. Furthermore, as the agent works, one can visually monitor and validate the process. 17 Nor is any knowledge of the latest security mechanisms necessary since the interface agent deals only with the web page interface not the encrypted streams between the client and server. For example, graphical user interface objects and windowing mechanisms typically remain constant ....

Kelly, J. L., A new interpretation of information rate, The Bell System Journal, July, 1956, pp. 917-926.

....m with non negative entries summing to one. The components of b i are the proportions of current wealth invested in each stock at time i. The conventional treatment of the problem of adaptive investment is grounded in the distributional approach to investment pioneered by Kelly (Kelly gambling [1]) and many others. This approach assumes the existence of an underlying probability distribution governing the sequence of price relatives (returns on gambles in the Kelly problem) Given knowledge of this underlying distribution, it is possible to specify a sequence of investment decisions or ....

....by a factor of S n = n Y i=1 b t i x i = n Y i=1 m X j=1 b ij x ij : 3) if the market performance is x n = x 1 ; x 2 ; x n ) 4) A sequence of portfolio choices b i constitutes an investment strategy or algorithm. To clarify, note that the well known Kelly gambling problem [1] can be expressed as a special case of the general investment setup as shown in [6, chapters 6 and 15] In Kelly gambling one must place bets on the outcome of an m valued event, such as the winner of a race with m horses. If the event takes on the value j (i.e. horse j wins) the gambler ....

J. L. Kelly, Jr. A new interpretation of information rate. Bell Syst. Tech. J., 35:917--926, 1956.

..... Then the increase in growth rate due to the side information is given by where the maximum is over all portfolio choices . Here denotes the alphabet for and is the dimensional probability simplex The idea of maximizing growth rate of wealth in the horse race market was introduced by Kelly [16]. In the general market, no closed form for the optimum portfolio or the optimum growth rate exists. Barron and Cover [6] showed that, in the presence of side information , the increase in growth rate is bounded above by where the growth rate and mutual information are both defined with logarithms ....

....portfolio in the horse race market. We first calculate the growth rate . Note that is minimized (and is equal to ) when . Therefore, the optimum portfolio is for The optimum strategy for the gambler is to bet in proportion to the underlying probability distribution. This was established by Kelly [16]. Proportional gambling is also known as Kelly gambling. The optimum growth rate is then given by (6) Now suppose the gambler has side information about the outcome of the race. We assume that and have a known joint distribution. Then the optimum portfolio is given by which results in the optimum ....

J. Kelly, "A new interpretation of information rate," Bell Syst. Tech. J., vol. 35, pp. 917--926, 1956.

....of the wealth on the entire sequence with side information is just the sum of the logarithms of the wealths generated by the K copies of the algorithm. 2.5 Related work Distributional methods are probably the most common approach to adaptive investment strategies for rebalanced portfolios. Kelly [16] assumed the existence of an underlying distribution of the price relatives and used Bayes decision theory to specify the next portfolio vector. Under various conditions, it was demonstrated (e.g. 5, 7, 6, 4, 2] that with probability one the Bayes decision approach achieves the same growth rate ....

J. L. Kelly. A new interpretation of information rate. Bell Systems Technical Journal, 35:917-- 926, 1956.

....of the wealth on the entire sequence with side information is just the sum of the logarithms of the wealths generated by the K copies of the algorithm. 2.5 Related work Distributional methods are probably the most common approach to adaptive investment strategies for rebalanced portfolios. Kelly [19] assumed the existence of an underlying distribution of the price relatives and used Bayes decision theory to specify the next portfolio vector. Under various conditions, it was demonstrated (e.g. 5, 8, 6, 4, 2] that with probability one the Bayes decision approach achieves the same growth rate ....

J. L. Kelly. A new interpretation of information rate. Bell Systems Technical Journal, 35:917-- 926, 1956.

....to support ourselves while doing so. I eventually decided to dedicate this talk to the person who first introduced me to serious research, to information theory, and coding, and to game theory. He was my first boss and mentor at Bell Labs, when I began work there as an undergraduate. His name was John L Kelly, Jr. After getting a PhD in mathematical physics from the University of Texas, John worked at Bell Labs for the rest of his life. He died of a heart attack in 1965 at the age of 41. Today, I ve decided to skim the surface of 4 different topics, all of which were of interest to John Kelly. I m ....

John L Kelly, "A New Interpretation of the Information Rate", Bell System Technical Journal, vol 35 #4, July 1956.

....to Theorem 1, we do not invest all or nothing in a relatively best object. Rather the optimal investment is a proportion, a k , of our fortune, where a k = kfi k Gamma n n(fi k Gamma 1) 3:2) It is to be understood that a k = 0 if fi k 1. This is just the Kelly betting system, Kelly (1956): For log utility, with an investment opportunity affording a return of fi 1 per unit invested with probability p and loss of the investment with probability 1 Gamma p, the optimal proportion of fortune to invest is a = pfi Gamma 1) fi Gamma 1) Here, if the kth object is relatively ....

J. B. Kelly (1956) A new interpretation of information rate. Bell System Technical J. 35, 917-926.

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J. Kelly. A new interpretation of information rate. Bell Systems Technical Journal, 35:917-926, 1956.

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Kelly, J. (1956), `A new interpretation of information rate', Bell. Sys. Tech. Journal, 35: 917-926.

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J. L. Kelly. A new interpretation of information rate. Bell Syst. Tech. J., 35:917--26, 1956. http://www.bjmath.com/bjmath/kelly/kelly.pdf.

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J. Kelly. A new interpretation of information rate. Bell Systems Technical Journal, 35:917--926, 1956.

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J. L. Kelly, Jr. A new interpretation of information rate. IRE Transactions on Information Theory, 2(3):185-189, September 1956.

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J. L. Kelly, Jr., "A new interpretation of information rate," Bell Sys. Tech. J., vol. 35, pp. 917--926, 1956.

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Kelly, J. (1956), `A new interpretation of information rate', Bell. Sys. Tech. Journal, 35: 917-926.

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Kelly, J.: A new interpretation of information rate. Bell Sys. Tech. Journal 35 (1956) 917--926

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J. Kelly, "A new interpretation of information rate," Bell Sys. Tech. J., vol. vol. 35, pp. 917-926, 1956.

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Kelly, J.L. (1956): "A New Interpretation of Information Rate," Bell Systems Technical Journal, 917-926.

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