The ligature in the fields of fixed income (bonds) and derivatives (mostly options) is extensive and fascinating. The other choices out there more complex. The flaws are well known - markets have fat tails. Normal distributions are used because they are a good simple introduction to the subject. People then to pick on the normal distribution, which I think is a little unfair. But I would expect the future of financial mathematics to proceed in this direction.Īlex_686 wrote:By "calculus of variations" do you mean "distribution of returns"? Distribution of future expected returns is the cornerstone of most investment and finance theory. It just makes sense to me that black scholes would itself be derivable under calculus of variations principles. And ultimately, black scholes is nothing but a heat equation, derivable from general principles of partial differential equations. Delta Hedging is performed with some of "the greeks" from the black scholes equation. Call options generally follow black scholes, or black scholes with minor tweaks. I wonder if the big banks are doing this kind of modeling. I know Ito Calculus is used extensively in financial mathematics, so i was just thinking that it make sense to extend calculus of variation principles to stochastic variables. Note this is an application of differential calculus (field of calculus of variations) to problems involving probability distributions (field of finance). Then again there is this, which is the first item that comes up when you Google "calculus of variations in finance." I am familiar with calculus of variations but not with enough background in financial mathematics to know if there is an application there. I'd like to be able to put it some practical use however in financial modeling. I've started getting into it lately, and its positively fascinating stuff. TomCat96 wrote:Just wondering if anyone here appreciates mathematics/physics and is knowledgeable in the calculus of variations, and if so, do you use it for any financial applications/modeling?
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