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频率,不确定性

相同一套做法,频率高比频率低有竞争优势。

  • 高频可以模拟低频,低频却不能模拟高频。
  • 高频比低频给你更详细的vision,反馈更快,偏差调整成本更小

不确定性也是分等级的。

 

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问题and答案

有一问题,需要解决方法,即答案。

有各种答案:

  1. 方法a能100%解决它,perfect
  2. 方法b100%不能解决它,也是perfect,至少你晓得一种不work的way,它暗示了此路不通,而且是明确的
  3. 方法c 50%work,50%不work
    这是个麻烦,某种程度上等价于0,似乎一切都回到原点
    但不是这样的
    它暗示了,有些未知的变量还没进入解答者的意识视野

    所以,3需要improve,它需要加入这些被忽视的变量,在此基础上被分裂成类型1,和类型2

question about 0|1 string

If there are 2 specific irrational 01 strings, is there a program which can take these 2 strings as input and output a rational string?

An intuitive answer is yes.

Another qurestion is for any 2 irrational 01 strings, is there a program which can make them to be a rational string?

Furthermore, is there a program to create a program to meet this need?

投资结果类型划分

股票很简单,它的基本操作就是买和卖。

一场投资活动有一系列基本操作组成。

一次基本操作只有两种

  • 以买开始,以卖结束
  • 以卖开始,以买结束

一群投资主体操作一只股票,如何从投资结果上划分这群投资主体呢?

第一个结论,那个赚得最多的主体=那个亏得最多的主体

假想这么一种情况,这场投资买卖没有时间限制

  • 有那么一个总是能赢的,每次基本操作都赚,简称股神
  • 有那么一个总是能输的,每次基本操作都亏,简称股痴

问股神存在吗?股痴存在吗?

直觉告诉我们,它俩都不存在。在这个意义上,股神=股痴。

那么应该如何划分投资结果类型呢?

  • 假设只考虑每次基本操作的盈利与否
    盈利=1       亏损=0
  • 一场投资活动由n个基本操作组成,为了讨论方便,假设n=10,而且要在规定时间内完成;即要在规定时间内完成10次基本操作,不多也不少
  • 那么只可能出现2^10=1024种类型
    X X X X X  X X X X X
    每个X=0|1

对任意一次投资活动,如果基本操作是盈利的,那么count++;如果亏损,那么 count–

根据count的大小来评定投资效果,count越大,越接近股神,count越小,越接近股痴。

很显然,count最大值是10,最小值是-10。count可能的取值包括(10,8,6,4,2,0,-2,-4,-6,-8,-10)

这就是一种划分,根据投资结果所做的划分,共11种类型,这种类型我们简称为R。

每种R类型都由若干子类型组成,子类型个数分别用N(10), N(8), N(6)等来表示。

问每种类型的子类型数目是多少?

10的情况也就一种,连续10个1,股神只有1个       🙂

-10的情况也就一种,连续10个0,股痴也只有1个  🙂

你看,股神和股痴1样多。   🙂

8的情况也就是10种可能性中出现1个0
-8的情况也就是10中可能性中出现1个1

这就是个组合嘛,熟悉二项式定理的都看出关系来了

N(10) = N(-10) = C(10, 0)  = 1

N(8) = N(-8) = C(10, 1) = 10

N(6) = N(-6) = C(10, 2) = 45

N(4) = N(-4) = C(10, 3) = 10*9*8/3/2 = 120

N(2) = N(-2) = C(10, 4) = 10*9*8*7/4/3/2 = 210

N(0) = C(10, 5) = 10*9*8*7*6/5/4/3/2 = 252

 

现在有1024个投资主体来从事这样的投资活动,假设是均匀分布的,那么每个投资主体只能找到唯一1个子类型,我们可以做上述R类型划分。

这种投资活动可以反复进行,分别对投资主体编号,对子类型编号,对R类型编号,我们就能研究投资主体的R类型变化情况。

如果某个主体在连续3次的投资活动中总是N(10),那么我们就有理由期待在接下来的投资活动中,他继续是N(10)。

如果某个主体在连续3次的投资活动中总是N(-10),那么我们就有理由期待在接下来的投资活动中,他继续是N(-10)。

注意,如果出现这种状况,那么其实股神真正等价于股痴,因为我们只要跟着股神走,就能赢;跟着股痴的逆方向走,也能赢。而且不仅仅是股神和股痴可以做为我们的领导,只要每个投资主体的连续投资结果是有规律可循的,都可以做为我们的领导。(这种规律不可能永远持续,但在某段时间内反复出现是可能的

 

为什么要做这样的类型划分? 因为这样可以跟踪研究投资主体,决定手头的资金使用权给谁比较合适。

谁适合做这样的类型划分? 券商交易软件合适,通用股票分析软件比如同花顺,大智慧也合适;手头有大把资金的却要寻找合适投资主体来代理的也合适;那些做模拟炒股的目的也在于此,希望找到合适的投资主体做为自己的领导:-);如果你想测量自己是否为领导,也可以来尝试:-)。

任给1棵树,都可以用表格来表示。

 

同样,任给1表格,也可以用树来表示。

When talking about speed, we must talk about time。

What is speed?   (speed = a kind of derivative)

  • speed=delta(something)/delta(time)
  • delta(something) = something1 – something0
  • delta(time) = time1 –time0

This is absolute speed.

There is another kind of speed,relative speed.

  • speed=delta(something)/(delta(time)*initial(something))

Take a look at this, http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/

It gives an excellent explanation of e.

In this article, we only talked about relative speed.  Relative speed = speed.

The e assumes relative speed to be 1.

e = (1+1/n)^n

Assumption:

  1. Start growing at 1
  2. a unit time period T, T=1
  3. The unit time period can splitted into smaller periods
    say N
  4. for its N periods, the relative speed = 1

There are N smaller periods.

  • If the growing counting mechanism is T, then growth only happens once
    We get 2
  • If the growing counting mechanism is T/2, then it grows 2 times
    (1+1/2)
    (1+1/2)(1+1/2)
    We get 2.25
     
  • If the growing counting mechanism is T/3, then it grows 3 times
    (1+1/3)
    (1+1/3)(1+1/3)
    (1+1/3)(1+1/3)(1+1/3)
    We get 1.3^3 = 2.370370…
  •   ……
  • If the growing counting mechanism is T/n, then it grows n times
    … …
    (1+1/n)(1+1/n)….(1+1/n) = (1+1/n)^n

See something here? 3 points here

  • the counting period count be split into smaller periods
                          N * T/N
  • newly growing parts could also grow
  • The growing relative speed keeps being 1 
    delta(something) = ((1+1/n)^n – (1+1/n)^(n-1))=(1+1/n)^(n-1) * 1/n
    delta(time) = 1/n
    initial(something)= (1+1/n)^(n-1)
    delta(something)/(delta(time) * initial(something))=1

This make sense:to get maximum growth we can do something in a smaller period to generate a smaller product but this smaller product can also join the process of growth。

 

 

Let us take a look at another kind of growth. In such kind of growth newly added product does not join the process of growth. Only the initial one grows。

  • If the growing counting mechanism is T, growth only happens 1 time, we get 2
  • If the growing counting mechanism is T/2, then it grows 2 times
    (1+1/2)
    (1+1/2+1/2)
    We get 2
  • If the growing counting mechanism is T/3, then it grows 3 times
    (1+1/3)
    (1+1/3+1/3)
    (1+1/3+1/3+1/3)
    We get 2
  •   ……
  • If the growing counting mechanism is T/n, then it grows n times
    … …
    (1+1/n+1/n+…+1/n)   1/n exists n times
    We get 2

Such kind of growth relative speed is not constant for its N periods when considering newly added parts。However when not considering newly added parts, its relative speed is 1.

http://news.163.com/special/tuling002/#!/scene-1

average

How many kinds of average number are there for a value depending on time series?

  1. simple moving average
  2. cumulative moving average
  3. weighted moving average
  4. exponential weighted moving average

Others?

EWMA is a very interesting one.

学科的起源

假如学科是图论,有的说欧拉解决了konigsberg问题后,图论就诞生了,天才欧拉在玩游戏。

也许有些学科是某些人玩游戏的结果(top-down),不过更多学科是由于实际问题导致的需求引起的(bottom-up)。