# Questions tagged [sde]

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### Transformation into Martingale

If $f$ is some function of BV on $\mathbb{R}$ and $dZ_t = f(W_t)dW_t + \mu_t dt$ ($W_t$ is a $1$-dimensional standard Brownian Motion), then what choice of real valued function $F$ makes: \begin{...
1answer
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### Swapping expectation operator with differential operator

Suppose I have a general SDE $dx_{t} = \mu dt + \sigma dz_{t}$ Then I can put $E[]$ on both sides to get $E[dx_{t}] = E[\mu dt] + E[\sigma dz_{t}]$ Now comes the question: I've seen some formulas ...
1answer
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### Question about the stochastic differential equation in the Merton model

in the following stochastic differential equation merton model we have $$\frac{ds}{s}=(\alpha-\lambda k)dt+\sigma dW+dq$$ where $\alpha$ is the instantaneous expected return on the stock; $\sigma^2$...
2answers
171 views

### Why can't I multiply two SDE Solutions?

SDE 1 is S1 = S10 exp( (r1-sigma^2/2) * dt + sigma dW1 ) S2 = S20 exp( (r2-sigma2^2/2) * dt + sigma2 dW2 ) E[dW1 dW2] = rho I want to price an option on S1 x S2 I know I need to use the SDE's to ...
1answer
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### Meaning of w in SDE

I'm missing meaning of $w$ in typical SDE like $dX_t(w) = f_t(X_t(w)) + \sigma(X_t(w))dW_t$, in context of $w \in F_{xxx}$. Does it mean that both $w$ is one of events that could happen before ...
1answer
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1answer
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### Bracket-Notation in SDEs

I often come across the following notation in my script, and I have not found it anywhere else. While our lecturer insists it is of utmost importance to write this way in his exams, he yet failed to ...