# Tagged Questions

Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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### Farkas’ lemma: purely algebraic intuition

Here is a statement of Farkas Lemma from the Wikipedia. Let $A$ be an $m \times n$ matrix and $b$ an $m$-dimensional vector. Then, exactly one of the following two statements is true: There exists ...
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### A (mathematically) sound investment strategy

It is common wisdom in the investment community that a long-term investor saving for his future would do well to invest in high-risk/high-return assets when he is young, slowly switching his portfolio ...
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### Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest bid,...
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### Rule of 72 doubling time

I need some help understanding this. So as far as I can tell. The rule of 72 is used to determine when prices will double in years. This is done by 72 divided by the rate, or interest. So it would ...
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### Repayments of a loan with compound interest

Suppose I have a loan of M dollars. At the end of each year, I am charged interest at rate R and make a repayment of P. The loan is repaid after n years. How long (n) does it take to repay the loan ...
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### If A can either increase by 100% or decrease by 50% with equal probability, what will be the arithmetic mean return over n periods?

This is more of a finance related question but deals with some discrete probability and or combinations. The question goes like this. If you buy stock A, and it has a 50% chance of going up 100% in ...
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### Compound interest: why does everyone get it wrong?

The compound interest formula is: $$A_t=A_0(1+r)^t$$ There is a simple derivation for this which works by starting with $A_1$ and then considering $A_2$ and then extrapolating. The above formula can ...
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### Does Change of Numeraire same as Change of Measure?

Does Change of Numeraire same as Change of Measure? It is a bit confusing since both looks same. Do they have same meaning, or just mathematically alike.
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### Isolating for i

So this might seem a bit fundamental, but in financial math the following equation gives you the price for a bond $$P = C \frac {1-(1+i)^{-n}} {i} + B(1+i)^{-n}$$ where $P$ is the price of the ...