Picture of author.

Benoit B. Mandelbrot (1924–2010)

Teoksen The Fractal Geometry of Nature tekijä

26+ teosta 2,358 jäsentä 25 arvostelua 5 Favorited

Tietoja tekijästä

Benoit Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and a Fellow Emeritus at IBM's Thomas J. Watson Laboratory.
Image credit: Mandelbrot at a TED conference in 2010 Photo: Steve Jurvetson

Tekijän teokset

The Fractal Geometry of Nature (1977) 898 kappaletta, 3 arvostelua
The Fractalist: Memoir of a Scientific Maverick (2012) 198 kappaletta, 2 arvostelua
Fractals: Form, Chance, and Dimension (1975) 195 kappaletta, 1 arvostelu
Penser les mathématiques (1982) — Avustaja — 31 kappaletta
Fractals and Chaos: The Mandelbrot Set and Beyond (2004) 31 kappaletta, 1 arvostelu
Fractales, hasard et finance (1998) 18 kappaletta
Nel mondo dei frattali (2005) 7 kappaletta, 1 arvostelu

Associated Works

The Science of Fractal Images (1988) — Avustaja — 134 kappaletta, 3 arvostelua
The Colours of Infinity: The Beauty, The Power and the Sense of Fractals (2004) — Avustaja — 56 kappaletta, 2 arvostelua
Discovery of Cosmic Fractals (2002) — Esipuhe — 24 kappaletta, 1 arvostelu
Classics on Fractals (1993) — Avustaja — 14 kappaletta

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Kirja-arvosteluja

There is a huge problem with the book, it is way to fun to read. This book is a different way of thinking about finance. The depth and breath of finance that Mandelbrot explains without simplifying the subject is almost unbelievable. This book starts with what the world of finance looks like, and then a way to fix it. Fractals are a very dynamic and simple way of modeling many different forms of turbulence from nature to finance. From dependence to power laws, fractals can provide a more realistic view of how markets behave.… (lisätietoja)
 
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Eugene_Kernes | 16 muuta kirja-arvostelua | Jun 4, 2024 |
Everyone should carefully read this text, the significance of Mandelbrot's points remains unfortunately as important as ever and still largely ignored by the average person.
Many aspects which we believe to be true measures or robust facts are actually, under the surface, ruled by distributions that can fluctuate wildly. What does an average price index of a stock mean, if the underlying distribution doesn't really have a mean?
 
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yates9 | 16 muuta kirja-arvostelua | Feb 28, 2024 |
Excellently written though poorly on-topic. Only the last four chapters (of 11 or so) had anything novel than a history of the industry. The meatiest two of these four chapters were difficult to follow, so poor marks there.

Ultimately, the points are depressing: 1) markets are riskier and more volatile than standard methods suggest, 2) (intrinsic) "value" is not really useful and 3) the reiteration that despite 150 years of research so far, we don't seem to know much more than that we don't know much.… (lisätietoja)
 
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eatonphil | 16 muuta kirja-arvostelua | May 8, 2022 |
A bit disappointing, but probably one of those books that is a victim of its own success. Perhaps when it was originally written, the views were considered more heretical than they are now. I would recommend that a close reader of taleb's anti-fragile and/or the black swan skip this book since taleb's works rehash the main thesis of Misbehavior (down to the self-aggrandizement, almost every time Fama is mentioned, Mandelbrot claims him as his doctoral student, and Mandelbrot spends a fair amount of time praising his own work/ describing his maverickiness [though to be fair, I suppose that's fair for a mathematician of his status]). In Misbehavior, Mandelbrot lays out the case against the foundational assumptions of modern portfolio theory, mainly its reliance on the gaussian distributions. Mandelbrot makes the simple observation that many of the observed drops in the markets should not have occurred under standard assumptions (technically the standard bell curve allows the possibility, but the chances are so remote that such events should not be observable in several billion lifetimes, let alone recurring several times in a few hundred years). Mandelbrot attacks the assumptions of normal distribution, independence of events, and constant volatility. Mandelbrot shows that the data just does not bear out the milder swings the normal distribution anticipates (that actual price data exhibit fatter tails than the normal distribution). Mandelbrot argues that analysis shows a long term dependence, that prices exhibit a certain type of memory that is endogenous but also moves are clustered. He develops a measure H, to show the persistence of momentum or anti-momentum as opposed to the standard random walk (which incidentally has an H of 0.5). Mandelbrot criticizes methods such as GARCH as building on a flawed foundation in fixing changing volatility. Instead Mandelbrot advocates the use of power laws, so-called Cauchy-levy functions and fractals in creating models. He claims that fractals, especially ones that accounting for trading time that stretch or compress can model price movements in a more accurate way. The work seems pretty technical, and Mandelbrot admits freely that research in using multi-fractal models is only developing. More interestingly (at least in my opinion) is the crash course lesson in fractals (the three steps to form a complex pattern, initiator, generator and rule of recursion) and measures of roughness. Mandelbrot believes fractals can be used to explain many naturally occurring phenomenon as well as complex systems as the economy.

On the whole, the book is written for a non-technical audience. Mandelbrot helpfully summarizes basic modern portfolio theory (from Bachelier's thesis on bonds, to Markowitz, CAPM (Sharpe), finally to Black Scholes). That portion was relatively well done, I thought it was a fair and accurate representation of what I had learned in basic finance in college. Mandelbrot also convincingly shows that the normal curve is not a good assumption, and that reliance on it can lead to blow ups. However, Mandelbrot is not as convincing when it comes to proposing fractals as a solution. Perhaps it's the limits of my technical knowledge, but it just did not seem convincing. On many parts of Mandelbrot's analysis, I just had to take him at his word that a certain analysis produced the conclusion he claims, despite his admissions at the end that scholars disagree over metrics like H. An interesting read, but it lacked the scholarly rigor to convince me that his solution could be the new foundation for risk analysis. The ideas seem to move and jump, seeming more like an interesting collection of Mandelbrot's works and thoughts rather than a coherent rigorous argument. On the other hand, I might not be able to understand a comprehensive scholarly defense without a deeper mathematical background. I suppose we'll never know.
… (lisätietoja)
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vhl219 | 16 muuta kirja-arvostelua | Jun 1, 2019 |

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