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I have some extreme cases in mind. With the kind of measure theory found, for example, in Shreve, I have no objection (or in Klebaner's Introduction to Stochastic Calculus with Applications).A problem Wilmott hints at -- or perhaps I'm reading this in -- is that naive quant students unwittingly become slaves to the tacit assumptions behind stochastic ideas (and other mathematical tools), not understanding that their use needs to be flexible and limited -- there's more happening in the markets than can be captured by the inflexible use of these limited mathematical constructs. It's all too easy for a quant to spend a lot of time obtaining a numerical solution to an SDE (for example), not knowing this may not be an appropriate tool for understanding what's happening "out there."And to make a point I've made before, what's happening "out there" has at a fundamental level been engineered by political decisions: that's where the "laws" of the market are ultimately coming from (barring short-term random fluctuations); not from the inbuilt structure of an SDE, martingale, or time series. It is very different in physics and engineering.
I have some extreme cases in mind. With the kind of measure theory found, for example, in Shreve, I have no objection (or in Klebaner's Introduction to Stochastic Calculus with Applications).
A problem Wilmott hints at -- or perhaps I'm reading this in -- is that naive quant students unwittingly become slaves to the tacit assumptions behind stochastic ideas (and other mathematical tools), not understanding that their use needs to be flexible and limited -- there's more happening in the markets than can be captured by the inflexible use of these limited mathematical constructs. It's all too easy for a quant to spend a lot of time obtaining a numerical solution to an SDE (for example), not knowing this may not be an appropriate tool for understanding what's happening "out there."
And to make a point I've made before, what's happening "out there" has at a fundamental level been engineered by political decisions: that's where the "laws" of the market are ultimately coming from (barring short-term random fluctuations); not from the inbuilt structure of an SDE, martingale, or time series. It is very different in physics and engineering.
