3153 Reputation

14 years, 316 days

Maximize Risk Adjusted Return in QP Matr...

Ok, first of all I renamed the return matrix R (A is allready used)
I now think I got two of them (minimize portfolio variance and minimize portfolio variance for a
given expected return in matrix form) figured out:

Cov := Matrix(CovarianceMatrix(R), datatype = float):
pr := .6*max([seq(ExpectedValue(Column(R, i)), i = 1 .. nstock)]):

A := Matrix([[seq(1, i = 1 .. nstock)]], datatype = float):
b := Vector([1], datatype = float):
Aeq := Matrix(...

Communication Mandelbrot...

Maple

When Benoit Mandelbrot was still alive I sent him an email:

Hi,
I am writing to you because I have trouble understanding why
the covariance function in the Fractional Brownian Motion (FBM) is given by:

(t[i]^(2*H)+t[j]^(2*H)-abs(t[i]-t[j])^(2*H))/2)

I would be very grateful if you could please explain this to me in simple and step by step terms.
I understand simple ARIMA models (P(t)=P(t-1)+E(t) where E(t)=p*E(t-1)+r(t)) which have the
same...

Cholesky Decomposition...

Maple

Ok If R is the Cholesky decomposition of the Covariance matrix then I need:

i) Cov=R*R'
ii) R'=R

I can show that i) indeed holds but ii) does not seem to work. Why?

restart:
with(LinearAlgebra):
Cov := Matrix([[.1, .2], [.2, 1.3]]);
Ap := LUDecomposition(Cov, 'method' = 'Cholesky');

Cov = Ap.Transpose(Ap);
Ap = Transpose(Ap)

Exponential Growth - Game Theory...

One thing I have always found interesting is that exponential growth/decay
is not symmetrical hence:

100*(1+0.01)^2+100*(1-0.01)^2-200 = 0.0200

For example:

If you start with 100 and bet 1% and you win and then again bet 1% of your portfolio value
and you win again your portfolio value will be PW=100*(1+0.01)^2.

If you start with 100 and bet 1% and you lose and then again bet 1% of your portfolio value
and you lose again your portfolio value will be PL=100*(1-0.01)^2. ...

permutations binomial random walk...

Ok, I want to generate a series like the one below:
I the first period the value is 0. In the second period
we can either move up one or down one. In the third
period given a down move in the last period we can
either move down again [-1-1] or we can move up [-1+1]
Given a up move in the last period we can
either move down [+1-1] or we can move up [+1+1]

[0]
[-1], [+1]
[-1-1],[-1+1],[+1-1],[+1+1]

Does there exist any maple command that does this?

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