Friday, December 26, 2008

The Kelly Criterion in Gambling, Investment and Innovation

The central problem for gamblers is to find positive expectation bets. But the gambler also needs to know how to manage his money. i.e. how much to bet. In stock markets the problem is similar but more complex. [...] In both these settings we explore the use of the Kelly criterion, which is to maximize the expected value of the logarithm wealth.
THE KELLY CRITERION IN BLACKJACK, SPORTS BETTING, AND THE STOCK MARKET by E.O. Thorp

Every risk taking could eventually fail. Even if you know of a positive expected outcome the random process can possibly work against you.
Throw a coin, bet on head - there is a 1:1 chance for head. The expected outcome is even - 50%. This is the margin of a positive expectation, less then 50% and the "odds" are against you.
Well, the betting odds are a different thing: the experts bookmakers or social aggregated estimation of probability on the outcome of an event. Lets say a bookie cannot measure the properties of a coin directly, he therefore needs to estimate the bias of the coin. It is unbaised 50% or does it tend in a certain percentage to head or tail?
The estimated propensity of an outcome, given by the bookie - or in case of an investment by the market are reflected in the reward rate, the odds.
If the bookie thinks the coin is baised so that in 100 throws, head comes up 60 times he could set the marginal odds to reward a tail with a 60/40-1 = 50% grand. A won 1€ bet will grant you 50 cents in addition to your stake of 1€. On average tail will come up 40 times in hundred, granting you a reward of 40% * 1.50 € - 60% * 1€ = 0 €. Neither the bookie nor you win a cent. The book is balanced. A interesting thing about averages is that they are a fictive measure in the shortrun. In our coin game, a fortunous series of hundred tails is still possible. A gambler who feels a different propensity of the game, just by experience or because of optimistic mood could assume a higher chance of win. Something could make me think that the coin is baised differently. Maybe I have better information than the bookie which makes me believe that head comes up 50 times in 100 throws. If I'm right this will give me on average an edge of 10%.

Wenn betting on head I gain 25 cent per throw.
50% 1.50€ - 50% 1€ = 25 cents

Still no one says that I cannot loose everything by pure bad luck.
Let's say I have a bankroll of 5€. Since I know I have an advantage of 10% I'm confident and put all in. 5€ on head. My wealth grows to 7.50 if in one case, I'm bankrupt in the other. I'm out of the game then. Most people then would say: don't bet now you know better. But if I'm not betting at all, we have the other extreme, 5€ for me no gain.
Somehow between loosing all and keeping my five euro there is the chance of multiplying my bankroll. If I bet long enough I should be able to take advantage of the 10% edge over the bookie.

The Kelly criterion finds the fraction of the bankroll that you need to invest to gain the maximum growth rate while mitigating the risk of going bankrupt.

The math shows that the optimal growth rate is the geometric mean of the probability distribution of returns.

A simplified Kelly formula is edge/odds, in ourcase this would result in 0.1/0.50= 0.2 as the rate of investment

Others have mapped the Kelly Criterion to Innovation, because its reasonable to see the funding of innovation as a game of chance.


Thursday, December 18, 2008

Afrikanische Zeitungen lesen ist mein neues Hobby, dank dem pressreader

Sunday, December 14, 2008

Saving some trees

Real Tree hugger now can use their iRex Reader to read over 800 newspapers, from derstandard to WSJ.

Its really comfortable, convenient and tree-saving.

Now its time to get serious with paperless office.

http://i-to-i.irexnet.com/2008/12/11/software-release-103-pressreader/

Monday, December 8, 2008

SOACon

So I was in Munich last week attending SOACon and W-JAX 08. What did I learn?
Alot about the tree letter word SOA.

SOA is distributed computing with different ownerships

Nicholai Josuttis

SOA is about breaking the monolith, it means full decoupling of units where the basic unit is the service. The Service is the basic unit of the development team, of the tests, of deployment, of versioning, of ownership (there is a business and a IT owner), of management and should be also of the unit for accounting

Stefan Tillkov

I see now that SOA is a partitioning approach for highly complex solutions that allows to handle the inherent complexity

Marcel Donges declared:
A SOA service is a business service, a attendance, a single "Dienstleistung" and there is no difference between a Dienstleistung and a SOA Service.


This thoughts have wide reaching consequences. For as in the past, without better knowing, I implemented webservices RPC style which binds the client heavly to the interface the server declared. SOAs in the contrary have such a loosley coupled interface that enhancements of the service barely change it.

A SOA is not a homogenous architecture and redudancy is allowed, as Josuttis explained, a serice oriented architecture will often not have one single customer service just because of what type of customer data you need will differ substanitally for every consumer. In reality services will have one consumer in average, many services will not be needed at all .
Maybe just one service will be very crucial, consumend by infinite systems, while the most will just have one consumer at best



x = number of producers; y= number of consumers


someone showed a powerlaw curve they distilled from empiric data. x = number of producers; y= number of consumers

A SOA is more the bazaar than the cathetral, we don't outline a efficient high level architecture, a big picture of our system but let free market forces decide which service to consume, which to spare.