]]>

]]>

"The American Put Option and Its Critical Stock Price" by David S. Bunch and Herb Johnson ?

Statistics: Posted by MAYbe — January 21st, 2017, 11:51 pm

]]>

http://www.wilmott.com/messageview.cfm?catid=38&threadid=99869&STARTPAGE=1

Statistics: Posted by MHill — June 29th, 2016, 1:15 pm

]]>

Statistics: Posted by Cuchulainn — June 13th, 2016, 8:31 pm

]]>

Statistics: Posted by QMichael — June 13th, 2016, 3:41 pm

]]>

In 1918 Einstein published the paper ÜBER GRAVITATIONSWELLEN [1] in which, for the first time, the effect of

gravitational waves was calculated, resulting in his famous quadrupole formula (QF). Einstein was forced to this

publication due to a serious error in his 1916 paper [2], where

scheme to solve the field equations of general relativity (GR).

accelerated charges emit electromagnetic waves, the linearized theory creates gravitational waves, popagating

with the speed of light in the (background) Minkowski space-time. A major difference: Instead of a dipole

moment, now a quadrupole moment is needed. Thus sources of gravitational waves are objects like a rotating

dumbbell, e. g. realized by a binary star system.

Statistics: Posted by Cuchulainn — February 12th, 2016, 10:59 am

]]>

]]>

]]>

For example if A is a 2[$]\times[$]2 matrix. Is it possible to present explicitly elements of of the matrix [$]e^A[$]? It might be written somewhere and not a difficult question.

For exp(Matrix) this might be a good start

Also, textbooks on ODEs will usually have a chapter or two on this subject. Best to start with simple examples.

It's a real deep theory. It underlies much of PDE/FDM. Depending on the structure of A, it might be possible to find an exact representation for exp(A) etc. Maybe the matrix is diagonalizable, then it becomes easy.

Statistics: Posted by Cuchulainn — February 10th, 2016, 6:36 am

]]>

2. This is a qualitative property of the solution that you should be able to prove without actually having a closed form. It is called the maximum principle in PD// It will be good. Also I have not worked much with matrices and actually could not understand quite simple questions. For example if A is a 2[$]\times[$]2 matrix. Is it possible to present explicitly elements of of the matrix [$]e^A[$]? It might be written somewhere and not a difficult question.

3. Its often happen in math that similar problem is simple and well resolved while what one is needed is a problem having not obvious solution.

Statistics: Posted by list1 — February 9th, 2016, 4:03 pm

]]>

Actually for about a month I look at SDEs from math point of view. I found a simple proof of the well known result and start to think about its generalization. I bumped with a technical difficulty which might be known or not as I am not sure about. It relates may be to closed form solution.

It is well known that solution of the linear sde admits closed form representation. Whether does this result is known for two dimensional case? Actually I need the result that states positiveness of the solution if the initial value is positive. I need it for pure mathematics. On the other hand it can be used in finance too as a model in which correlated indexes or currencies are modeled by multidimensional system of SDEs. I will appreciate to a suggested hint.

I find the term 'pure mathematics' a bit artificial.

Quote

states positiveness of the solution if the initial value is positive

This is a qualitative property of the solution that you should be able to prove without actually having a closed form. It is called the maximum principle in PDE.

//

BTW the bespoke calculus of variations example and 'solved' by the Euler equation was discovered e as follows:

Quote

In solving optimisation problems in function spaces, Euler made extensive use of this `method

of finite differences'. By replacing smooth curves by polygonal lines, he reduced the problem of

finding extrema of a function to the problem of finding extrema of a function of n variables, and

then he obtained exact solutions by passing to the limit as n ! 1. In this sense, functions can

be regarded as `functions of infinitely many variables' (that is, the infinitely many values of x(t)

at different points), and the calculus of variations can be regarded as the corresponding analog of

differential calculus of functions of n real variables.

Statistics: Posted by Cuchulainn — February 9th, 2016, 11:03 am

]]>

It is well known that solution of the linear sde admits closed form representation. Whether does this result is known for two dimensional case? Actually I need the result that states positiveness of the solution if the initial value is positive. I need it for pure mathematics. On the other hand it can be used in finance too as a model in which correlated indexes or currencies are modeled by multidimensional system of SDEs. I will appreciate to a suggested hint.

Statistics: Posted by list1 — February 6th, 2016, 6:37 pm

]]>

QuoteOriginally posted by:Cuchulainn

What about finding y(x) that minimizes the length of the curve:

Is there a closed solution?

Quote: An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. First, our problem does not applicable as far as it starts with minimization of the integral but closed form should originated by equation. On the other hand we should look in which terms the solution of the problem is represented.

How are you getting on?

Statistics: Posted by Cuchulainn — February 6th, 2016, 6:00 pm

]]>

What about finding y(x) that minimizes the length of the curve:

Is there a closed solution?

Quote: An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. First, our problem does not applicable as far as it starts with minimization of the integral but closed form should originated by equation. On the other hand we should look in which terms the solution of the problem is represented.

Statistics: Posted by list1 — January 19th, 2016, 10:54 am

]]>