Renter - page 15
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
Hello all!
I have been allowed to use a deposit of X0 rubles for t months. Every month a fixed percentage q of the current value of the deposit X is deposited. I'm allowed to withdraw a percentage k from the account every month, but it doesn't exceed the value of q.
So the task is to maximize the amount of money withdrawn over a period of t months. It seems obvious that withdrawing the whole accrued interest q every month is not the best option, because in this case the deposit does not grow and with less load on the account, the eventually withdrawn amount may be larger... On the other hand, the value of k should not go to zero, because in this case the amount withdrawn would also go to zero. Apparently, the truth is somewhere in the middle. But where exactly?
Help me solve this problem analytically in general form.
P.S. I didn't post any problems not related to trade, because the proposed topic is related to the latter.
I deliberately quote the whole post by the respected Neutron, so that my proposal can be compared with the ToR.
"I am allowed to withdraw a certain percentage k from the account each month, which does not exceed the value of q".
The percentage k does not exceed q, but it may well be variable. This makes the problem extremely complicated, but makes it much more interesting. It is a problem of calculus of variations. This is the problem I am going to solve.
I deliberately quote the entire post by the respected Neutron'a so that my conclusion can be compared with the ToR.
"I am allowed to withdraw every month a certain percentage k from the account, which does not exceed the value of q".
The percentage of k is less than q, but may well be variable. This makes the problem extremely complicated, but makes it much more interesting. This is the problem of calculus of variations. This is exactly the problem I'm going to solve.
Alexei!
Bravo.
That's right.Since the requirement of cacheflow, propor- tional to anything, at any given moment, is artificial...
Really, if this, something is not a universal curve...
;)
is the universal curve an exponent or what?
Yeah...
But the key to the problem, it seems to me, is that there are several of them (curves).
and only if the "younger one" is ahead of the "older one" will the fanoman be.
Unfortunately, the whole example is without flow discounting, which (discounting) kills any effort.
But! for a foregame where %%day or 15minute weighting is sometimes ;) - there are solutions.
With unflagging interest, I am following the ASUTP.
;)
Unless, of course, it's for sport, yes.
I'll just have to take my humble leave.
PS The ACS methods proposed by avtomat are also numerical optimization methods, if, of course, I understand him correctly.
Yes ;)
Go for it. The problem is interesting.
Numerical methods have already solved it, but I want to pick it apart ;)
I deliberately quote the entire post of respected Neutron'a, so that my proposal can be compared with the ToR.
"I am allowed to withdraw every month a certain percentage k from the account, which does not exceed the value of q".
The percentage of k is less than q, but may well be variable. This makes the problem extremely complicated, but makes it much more interesting. This is the problem of calculus of variations. This is exactly the problem I'm going to solve.
I agree, it's more interesting. But the original problem is not as simple as it seems at first sight.
The trick is hidden in the feedback.
with unflagging interest in the ACSPS.
;)
for sure ;)
Let's continue...
.
In the previous step the function
determining the amount of accumulated withdrawals over time.
.
Let us rewrite it in the following form
and treat the input quantities as parameters.
It didn't work out very well. I won't post the calculations here. There is nothing beautiful about them.
I tried to use the following observation: 1+q-k = 1+epsilon, epsilon being a small value. Then I expanded the derivative by k in Taylor's series, first holding terms up to the third order of smallness. Then, after simplifications, we got the cubic equation. I discarded the third-order smallest term and tried to solve the resulting quadratic one. I failed: the discriminant is positive only at small t.
I'm afraid that I made a mistake by rejecting the cubic term: although it is a term of the third order of smallness in epsilon, it is not small. I had it as follows: epsilon*epsilon*(epsilon-q)(t-1)(t-2)(t-3). It can be seen that for large t it can be quite small (even if epsilon~0.01 is quite a realistic assumption). And one does not want to solve the cubic one.
Let's see what Oleg gets.
P.S. Assuming epsilon*t = O(1) (or q*t = O(1) ), you can approximate the power function by an exponent. Let's try it.
There is another approach - without Taylor series, but simply by tangent method (Newton's method, I think). And a fairly exact analytical solution can also be obtained.