Stochastic Processes Quotes

Life cannot be calculated. That's the big mistake our civilization made. We never accepted that randomness is not a mistake in the equation -- it is part of the equation.

Briefly speaking, our conclusion is that stochastic volatility does not make a huge difference as far as the pricing is concerned if you get the average volatility right. It makes a big difference as far as hedging is concerned.

Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.

Randomness works well in search sometimes better than humans.

The true law of economics is chance, and we learned people arbitrarily seize on a few moments and establish them as laws.

The model used by Wall Street to price trillions of dollar's worth of derivatives thought of the financial world as an orderly, continuous process. But the world was not continuous; it changed discontinuously, and often by accident.

We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?

Maximum of an average is necessarily less volatile than the average maximum.

Almost all life depends on probabilities.

In mathematics, as in physics, so much depends on chance, on a propitious moment.

You get pseudo-order when you seek order; you only get a measure of order and control when you embrace randomness.

I tried to develop some theories that took account of the uncertainty in the world and the complexity in the world.

On the theoretical side, I was concerned with stochastic resonance.

Knowing the importance of luck, you should be particularly suspicious when highly consistent patterns emerge from the comparison of successful and less successful firms. In the presence of randomness, regular patterns can only be mirages.

I've debated many economists who claim to specialize in risk and probability: when one takes them slightly outside their narrow focus, but within the discipline of probability, they fall apart, with the disconsolate face of a gym rat in front of a gangster hit man.

Random questions are the least random of all questions.

Whatever way uncertainty is approached, probability is the only sound way to think about it.

That economic decisions are made without certain knowledge of the consequences is pretty self-evident. But, although many economists were aware of this elementary fact, there was no systematic analysis of economic uncertainty until about 1950.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

The grand assertion is that you must see the world through probability and that probability is the only guide you need.

Probability but no truth, facility but no freedom--it is owing to these two fruits that the tree of knowledge cannot be confused with the tree of life.

Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.

Probability is the very guide of life.

Our starting point then was trying to find a way to incorporate mean reversion into the HoLee model.

In the nature of the use of chance operations is the belief that all answers answer all questions.