Can Somebody solve the Rich Investor's Paradox?

[WWW Mechanical PE]

The Rich Investor’s Paradox

Let us assume you have been given an immense amount of money and you are worth $50 billion. In addition you have a clairvoyant that can read tomorrow’s edition of the Wall Street Journal. You decide to start investing in stock because you believe you have a sure thing. Now a fundamental-assumption in derivatives theory says all investor thinking is embedded in the market-pricing and hence the stock-market is omniscient. In addition all physical laws say a cause is required for every effect in a deterministic way.

Now consider 3 Cases:

Case 1

The clairvoyant looks in his crystal ball, reads off the stock prices, and sees 6,631,257 million shares of ABC company traded tomorrow with the price going up by $4.25 per share. ABC company is worth let’s say around $5 billion. You want to test his ability to predict, so you secretly decide to buy 100,000 shares today at around $20/share. The next day everything is exactly correct, and determinism appears to be working.

Case 2

So the next day your clairvoyant looks in his crystal ball, goes through the list and sees ABC Company with 19,925,918 million shares with the price going up by $30 per share, and you say whoa! You secretly order 15 million shares. The next day the headline reads right on target to the very last number of shares traded, but your order couldn’t execute on 5 million shares. The market couldn’t absorb that many trades in a day. You figure out that you’re just driving the price around with market purchasing power, and probably won’t make a profit when you sell-off. Determinism appears to be working.

Case 3

The clairvoyant was exactly right both times, but you aren’t making money the way you thought you would. So you plan your next move secretly, and decide to buy-out XYZ company (a different company) if the clairvoyant sees a drop in the price of XYZ as he takes his readings every morning. Your secret buyout price is considerably higher than the market valuation of the stock, and you wait it out with your hidden plan in place. a) Does the stock price rise to your secret buyout price? or b) Could the clairvoyant possibly read a price-drop, and then you buyout the stock as planned which in turn drives the price higher instead? With item 3a) it appears you can move the market price without doing anything and with item 3b) the clairvoyant's reading is wrong. Or perhaps your choice has no physical consequence either way, though billions of dollars are involved. That's the paradox.

 

[BvU]

Where's the paradox ?

 

[WWW Mechanical PE]

Where's the paradox ?

Thank you. I edited the OP so it's more clear now.
Case 3 appears to be a paradox with supposedly perfect information about the future assuming determinism.
If you have more questions please let me know.

 

[BvU]

Stilll no paradox

 

[PeroK]

The existence of the clairvoyant takes the issue out of the realm of mathematical analysis.

 

[Stephen Tashi]

Suppose we attempt to define a sequence of real numbers $a[0],a[1],a[2],...$ with the following properties:
$a[0] = 1$ and if $a[n+1] < a[n]$ then $a[n+1] = a[n] + 1$.

No such sequences of real numbers exist with a term such that $a[k+1] < a[k]$, but this is not a paradox. If you assume some physical situation exists that is modeled by the above properties and has $a[3] < a[4]$ then you'd have a physical paradox.

 

[EnumaElish]

At time 0 the price of XYZ is $10/share. At time 0 you resolve "I shall buy XYZ shares at $20 as soon as the clairvoyant predicts a price drop." Then T periods elapse and XYZ's price goes up to $30. One day the clairvoyant sees a tumble. You offer $20 but nobody's selling. You sell short like crazy at $20, forcing a drop. Then you buy it back at $20. No paradox. Also no profit.

 

[mfb]

You don't need the stock market. Ask the clairvoyant how many fingers you will show, and then show a different number.
The classical grandfather paradox, and the possible solutions to it are all well-studied. With the additional option of "the clairvoyant can be wrong".

 

[Nugatory]

This problem is a variant of Newcomb's Paradox: https://en.wikipedia.org/wiki/Newcomb's_paradox