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Probability and Finance: It's Only a Game!
Provides a foundation for probability based on game theory rather than measure theory.
440 pages, Hardcover
First published June 15, 2001
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January 25, 2016
This is advanced math book, so it can easily break brain for unprepared,but that doesn't mean it can't be summarized into more simple philosophical statements. I put this book into my top 1% "game changers" list.
1. You will not get rich without risking bankruptcy. More broadly, you should bet more (or risk more) than you have if you want X.
2. "If reality plays against you, you can give valid sequential probabilities (based on moves, without probability distribution) and you can use them to make optimal decisions." A lot of (novice) Sceptics believe they should know the future when actually they don't.
3. If Sceptic can weakly influence E, he can influence E (on another round). (Redefining second point.)
4. "Changes in market prices over an interval of time of length dt scale as √dt." If Reality doesn't obey this rule, a Sceptic can make a lot of money.
5. You can still make forecasts (based on your previous successful outcome) about reality even if you know nothing about the reality.
6. The expected value of (dS(t))2 just before
Market makes the move dS(t) is approximately sigma2S2(t)dt.
A bit more precise examples from book:
Why stock prices movements look like brownian motion? "Market can avoid allowing Investor to become infinitely rich only by choosing his dS(t) so that S(t) [martingale] has variation exponent exactly equal to 2 [look like random]."
Market game, one move:
1. Market announces S(0) > 0.
2. Investor announces sigma(t) [holdings]
3. Market announces dS(t)
4. Market outcome: S(t+dt) = S(t) + dS(t).
5. Investor outcome: I(t+dt) = sigma(t) + S(t)dS(t)
And much more... Read the book two times.
1. You will not get rich without risking bankruptcy. More broadly, you should bet more (or risk more) than you have if you want X.
2. "If reality plays against you, you can give valid sequential probabilities (based on moves, without probability distribution) and you can use them to make optimal decisions." A lot of (novice) Sceptics believe they should know the future when actually they don't.
3. If Sceptic can weakly influence E, he can influence E (on another round). (Redefining second point.)
4. "Changes in market prices over an interval of time of length dt scale as √dt." If Reality doesn't obey this rule, a Sceptic can make a lot of money.
5. You can still make forecasts (based on your previous successful outcome) about reality even if you know nothing about the reality.
6. The expected value of (dS(t))2 just before
Market makes the move dS(t) is approximately sigma2S2(t)dt.
A bit more precise examples from book:
Why stock prices movements look like brownian motion? "Market can avoid allowing Investor to become infinitely rich only by choosing his dS(t) so that S(t) [martingale] has variation exponent exactly equal to 2 [look like random]."
Market game, one move:
1. Market announces S(0) > 0.
2. Investor announces sigma(t) [holdings]
3. Market announces dS(t)
4. Market outcome: S(t+dt) = S(t) + dS(t).
5. Investor outcome: I(t+dt) = sigma(t) + S(t)dS(t)
And much more... Read the book two times.
Displaying 1 - 1 of 1 review