Internet And Money

asserted that binary digits could be transmitted over a noisy channel with
an arbitrary small probability of error if the binary digits were suitably
encoded.
• In 1956 a scientist working for Bell Labs, John Larry Kelly, Jr., brought
together game theory and information theory when he published ‘A new
interpretation of information rate’1 (Kelly 1956). He showed that in order
to achieve maximum growth of wealth, at every bet a gambler should
maximize the expected value of the logarithm of his capital, because it is
the logarithm which is additive in repeated bets and to which the law of
large numbers applies. The assumptions are that the gambler’s capital
is infinitely divisible and all profits are reinvested. Money management
systems which maximize the expected value of the capital are said to
employ the Kelly criterion.
• Bellman and Kalaba (1957) considered the role of dynamic programming
in statistical communication theory and generalized and extended (Kelly
1956)’s results.
• The first to introduce the Kelly criterion in an economic context, Latan´e
(1959) showed that investors should maximize the geometric mean of their
portfolios.
• Breiman (1961) proved that using the Kelly criterion is asymptotically
optimal under two criteria: (1) minimal expected time to achieve a fixed
level of resources and (2) maximal rate of increase of wealth. It is only in
continuous time that the results are exact.
• In 1962, Edward O. Thorp, an American maths professor, author and
blackjack player wrote Beat the Dealer (Thorp 1962), which became a
classic and was the first book to prove mathematically that blackjack
could be beaten by card counting.
• Thorp and Walden (1966) developed a winning strategy for a side bet in
Nevada Baccarat and used the Kelly criterion to determine bet sizes.
• Thorp (1969) concluded that the Kelly criterion should replace theMarkowitz
criterion (Markowitz 1959) as the guide to portfolio selection.
• Hakansson (1970) consider the optimal investment and consumption strategies
under risk for a class of utility functions and also give the necessary
and sufficient conditions for long-run capital growth.
• Radner (1971) was the first to employ a balanced investment strategy in
the context of stochastic generalizations of the von Neumann model of
economic growth.
1The original title was ‘Information theory and gambling’, but Kelly changed it to appease
his employer.