Welcome Uwe from Germany. It is a pleasure to have you on the WIND thread.
>Is there a book on the subject of game-theory (e.g. Gambler's Ruin)
>as applied to investing?
From Markowitz's classic Portfolio Selection (required reading) on there are numerous books covering what has become traditional approaches to asset allocation, but I confess to not being aware of any that focus on the approach I presented, although they probably exist. All the tools needed (Utility Theory, Probability Theory, Optimization) are traditional and readily available in book form.
Incidentally, while the Gambler's Ruin problem I presented sounds like it is derived from Game Theory, it is not. Game Theory focuses on beating an intelligent opponent countering your every move, but the investment problem I solved concerned a non-adaptive, albeit random, real-world. I have never had much use for formal Game Theory, although I can imagine instances where that could change, even in investing.
Here's an additional tidbit. As an Economics student reading background material for his dissertation in the early fifties, Markowitz writes he was influenced by the work of John Burr Williams, in which it was recommended that a stock be valued by discounting its future dividends. Markowitz realized that, in an uncertain world, a stock should be valued by its expected present value, and similarly for a portfolio of securities. But he also perceived instantly that to maximize the expected value of a portfolio would always result in concentrating the total investment in the single stock with the highest expected present value. Markowitz knew from his "common sense" and other readings that this was wrong, and that one should diversify to reduce investment risk. This was the seminal observation that led to the development of traditional asset allocation.
Markowitz's genius was to focus the investor on controlling risk, mainly through diversification, rather than maximizing return. By the time Warren Buffett and other pariahs (i.e. statistical outlyers) scoffed at that approach, my guess is they encountered an entrenched academic bureaucracy, which had no interest in re-examining fundamentals. But the irony is that Markowitz's seminal observation that maximizing expected portfolio return automatically resulted in investing all of one's capital in a single company was dead wrong. By the time he completed his dissertation, had he thought two seconds about it, he would have realized that his initial perception was limited to insignificant circumstances in which the investor has a linear utility for money in the range of probable portfolio outcomes. Thus the launching of a whole industry for controlling investments, to this day influencing probably trillions of dollars of investment decisions, occurred because a student erroneously applied his mistaken common sense to something about which he knew little. Unfortunately, he was extremely capable and applied his skills all too well.
Allen |
