Quantitative Finance Stack Exchange
Quantitative Finance Stack Exchange

Questions tagged [mathematics]

Used for question on application of mathematics in finance - from interest calculation to mathematical description of random processes.

199 questions
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What is exactly Euler's decomposition?

I have often seen the following statement in different paper: As $\sigma$ is homogeneous and of degree 1, we use Euler decomposition and write $\sigma(x)=\sum_{i=1}^n x_i \frac{\partial \sigma(x)}{\partial x_i}$ The thing is, I am trying to find…
SRKX
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1 answer

application of lie groups in finance

Can some one kindly go over some of the applications and use of Lie groups in finance? The math is very rigorous and I don't fully understand it or the potential it could have. Let me share some examples with you, I'm sure there are many more. There…
pyCthon
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7
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Implications of the Riemann hypothesis in finance?

I was recently at a seminar by a top hedge fund manager at a top university for finance students, when one of the finance professors asked him what do you think are important areas of research for my PhD students. The hedge fund manager responded…
pyCthon
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4
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Clarify a derivation in Pat Hagan's Convexity Conundrums

I am looking for help in understanding the algebraic derivation to go in between some of the lines in Pat Hagan's famous Convexity Conundrums paper e.g. how he goes from 3.4a to 3.5a.
Randor
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3
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2 answers

Preparation for interview: influx of power of the moon

I am preparing myself for an interview for a quantitative analyst position and one of the sample questions asked in previous examinations was: "Suppose the moon were to disintegrate, and fall to earth over 5000 years. How does this influx of power…
Giuseppe
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How can I express this sum in a easier way?

For instance, I know that the sum of the first $101$ natural numbers can be expressed in the following easy computation: $\sum_{i=1}^{101}i = \frac{101*102}{2}$ One of the questions is: and what about this sum? $\sum_{i=1}^{101}i +…
Nobody
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Optimal stop-loss reinsurance

What are some methods for optimizing stop-loss reinsurance? I've found an article on the minimization of the variance. I also know about the method of average-at-range. Can we apply a method for single-level contract KNST stop-loss?
Vladislav
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Is there a formula for future value of a growing annuity with yearly payment growth and monthly payments?

My example is saving for college: assume a start of 0 balance deposits of 200 made monthly, every year they increase by (g) 2% to account for salary increases, first deposit made at the end of the first month Interest Rate (r) is constant at 8%…
plockc
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What is the right group of durations?

It seems that the group of durations commonly used in quantitative analyse is $\mathbf{R}$ but it seems to me that $\mathbf{R_+^*}$ could also be an interesting choice. While I am not aware of explicit references to $\mathbf{R}$ as the group of…
user40989
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Does it make sense to apply complicated mathematics to calculate with precision when the margin of error is +/-10%?

This is more of a philosophical question than general question. Quantitative finance applies highly complicated mathematics and has attracted very smart people to this field lately given the high pay banks are willing to pay for such talent.…
curious
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Proxy for a trigonometric angle function

You can't calculate an actual/real angle with the sine function with discrete market data. I need a substitute value for inputs that require an angle value. If you're only calculating the angle between two adjacent bars, is it possible to use the…
montyhall
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