Renter - page 31
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Neutron:
There is also the question of how often withdrawals should be made (once a year, once a month or once a week). If you play with the parameters (of course, the value of q will change), the optimum is the most frequent withdrawal, which is limited by the percentage of withdrawal fees.
I think you have again got the "optimum" solution wrong and unsubstantiated.
Reshetov, and then me, showed by a reduced formula - that the optimal withdrawal is closer to the end of the term. Thus, it seems to me (I also have no time to prove it), that the optimal withdrawal would be atCourt and at the end...
;)
Just a reminder: Mikhail Andreyevich, without bothering to comment, posted the "solution" here.
There too, the conclusion about the proportion is wrong.
The next page shows it.
here's the one with the reinvestment cut-off time, sort of strictly.
;)
FreeLance:
I think that once again, an unsubstantiated and incorrect 'optimal' solution has been obtained.
Reshetov, and then me, have shown with a reduced formula - that it is optimal to withdraw closer to the end of the term. Thus, it seems to me (and I have no time to prove it, either) that the optimal withdrawal would be atCourt and at the end...
Perhaps you and Reshetov are right.
I justified my statement by incorrect formula obtained above before Alexey's comment. If you use the correct dependence for the amount of withdrawals obtained a few posts above, the picture is as follows:
Here is the dependence of the amount of funds withdrawn from the account normalized to the initial deposit amount for time t = 100 months. This is the red line. You can see a clear maximum at k=0.4q. The blue line shows the result for the case when we withdraw funds 100 times more often. There is no difference.
Thank you, Mikhail Andreevich, for your valuable remark.
Perhaps you and Reshetov are right.
I justified my statement by the incorrect formula obtained above before Alexey's comment. If you use the correct dependence for the amount of withdrawn funds obtained a few posts above, the picture is as follows:
Here is the dependence of the amount of funds withdrawn from the account normalized to the initial deposit amount for time t = 100 months. This is the red line. You can see a clear maximum at k=0.4q. The blue line shows the result for the case when we withdraw funds 100 times more often. There is no difference.
Thank you, Mikhail Andreyevich, for your valuable remark.
Thank you for the zigzag problems!
They are trade-related, and the answers are not always obvious...
;)
Here are the results of numerically solving the resulting equation for an average deposit lifetime of 1 year. We assume that we withdraw funds once a month according to the optimal scheme.
On the abscissa axis is plotted the average percentage q of the deposit's rise per month, ranging from 1% to 100% on a logarithmic scale. The blue line shows the optimal percentage (of interest accrued) of kOpt withdrawal that maximizes the amount of money withdrawn over the year (as a fraction of the original deposit - the red line).
It may be noted that at growth rate of the deposit less than 17% per month, it is more profitable to withdraw more than it accrues (blue line over 1)! In other words, in this situation, it is better not to open a deposit, or by the expected time of death of the deposit, withdraw more than it was not possible. But, at q>17%, it is better to withdraw less than q, while we will have time to withdraw more than we deposited (red line) and will be in profit.
It is interesting that the deposit itself in this situation is growing like a rocket, while our deductions into our pockets is much slower... See Fig. At 100% per month (well, for example), we have a pocket profit 200-300 times compared with investment, and here is our deposit before the death grows as much as the moon: 2^12=4000 times. And we cannot improve anything! - After all, we do not know for sure, when we have to stop and save the deposit. Therefore, we have to make do with what we have time to withdraw according to our optimal system. Do you understand what I'm saying? This fact seems to explain a lot of existing myths about Forex. For example, the apparent huge growth rate of funds (after all, look at the deposit), with almost total "poverty" of the vast majority of traders. The paradox is easy to explain: we look at the deposit growth curve, and we have to live on what we have managed to withdraw and, as a rule, we do not have time to withdraw anything.
I think that this example for the special case of t=12 months, although it is idealized to the extreme, is very interesting for analysis and further reflections.
Withdrawal_(together_with_interest_which_should_be_coming_up) = Accrual_without_drawal - Depo_at_end_period_t
The formula is the same, but including interest. Now it should add up. I'll check it tonight.