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Compound Interest Including contributions

The initial one-off payment is compounded for all $10$ periods, so at the end this becomes $$\$1000 \times(1+15\%)^{10} = \$4045.56$$ The $10$ annual contributions of $\$200\times 12$ each are ...
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Intuition of convex combination of probability measures.

Let $X,Z$ be random variables on $(\Omega,\mathscr{F},P)$. Let $Z\sim \textrm{Bernoulli}(\lambda)$. The above convex combination has the following probabilistic interpretation: for $A \in \mathcal{B}(\...
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Compound interest computation on a "non continuous" asset

As Wolfram Alpha gave it $$\sum\limits_{n=N}^{k}\frac{X}{Yn}=Z \implies \psi (k+1)=\psi (N)+\frac{Y Z}{X}$$ Using harmonic numbers instead $$H_k=H_{n-1}+\frac{Y Z}{X}=A$$ Assuming that $k$ could be ...
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Analysing Geometric Brownian Motion

I will provide here analytic results with which one can compare a (good) simulation. The SDE of a GBM is $dX_t=\mu X_tdt+\sigma X_t dW_t,\,X_0>0$. The solution is found by applying Ito to $f(x)=\ln ...
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