If asset prices are primarily driven by information arriving in the market and since this information is by definition unknown until it arrives it is fair to view prices as random.
This is nonsense. Just because you personally didn't figure something out in advance doesn't mean it was random. It especially doesn't mean that future price movement is completely independent of past price movement.
For example, there was a time period where personal loans to Elon Musk backed by his stock holdings would have been subject to a collateral call if the stock fell below a certain price. The founder of a large company having to liquidate a portion of their holdings would significantly affect the price of the stock.
This nonsense is like saying "I couldn't predict the results of a sealed bid auction therefore the results are random."
The result of the auction were determined 100% by the bids and thus not random at all. Each one of those bids was submitted by bidders making and deliberate choice and therefore also not random. If you made an effort to identify the bidders and their economic situations, you might have been able to predict the resulting price.
I would actually predict that as t approaches infinity, the value of a stock approaches it's shareholder retained value plus discounted future earnings divided by outstanding shares.
If the markets were truly random this number should be very close to 100%