# Tag Info

## Hot answers tagged stochastic-calculus

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### Bond Price expression

If $\delta > 0$ is very small, then the interest incurred during the small subperiod $[t, t + \delta]$ can be approximated using the simple interest formula. More specifically, the interest ...
• 480

### Do real life economists and financial analysts actually use calculus in their jobs?

I have never used calculus in my non-academic jobs. I didn't do sports, speak German (except when socializing), program Excel VBAs or directly apply what I have learned about product line management ...
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### Do real life economists and financial analysts actually use calculus in their jobs?

Yes, whether you do research and you need to study a new model and characterize optimal behavior, or if you are studying data and you are estimating any model that is not linear you use calculus on a ...
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### What exactly is/How exactly do we interpret the binomial model's Radon-Nikodym derivative?

In economics, the Radon-Nikodym density $\frac{d \mathbb Q}{d \mathbb P}$ of the risk-neutral measure $\mathbb Q$ with respect to the physical measure $\mathbb P$ is the price of Arrow-Debreu ...
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### Given $\mathbb Q$ and $X_t$ is $\mathbb Q$-Brownian, find $\frac{d\mathbb Q}{d\mathbb P}$ / Uniqueness of Brownian or Radon-Nikodym derivative

As you say (how did $\sin t$ in the initial problem become $\cos t$?), $\mathbb{Q}$ is a measure under which $W_t$ becomes $\tilde{W}_t - \sin t$, where $\tilde{W}_t$ is a $\mathbb{Q}$-Brownian motion....
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$$dx_t = \mu dt + \sigma dz_t \\ y_t = f(t, x_t)$$ A key idea here is that $\left( dx_t \right)^2=\left( \ldots \right)dt^2 + \left(\ldots\right) dzdt + \sigma^2 dz_t^2 = \sigma^2 dt$. The loose ...
I think there should be a minus before the final term in the expression you are looking for. In any case, you did not plug in the optimality condition for $w$, which is in your case  w = -\frac{V'(A)...