# Questions tagged [expected-value]

The tag has no usage guidance.

16 questions
Filter by
Sorted by
Tagged with
461 views

### Why is logarithmic mean equal to the arithmetic expectation less one-half its variance?

I've taken it as gospel that the following equality is true: $$\mathbb{E}[\mu_x] = m_x - \frac{1}{2}\sigma_x^2$$ where: $\mathbb{E}[\mu_x]$ is the expected value of the logarithmic mean of some ...
108 views

### How to calculate the expected stock returns for an individual stock?

I know about CAPM. My question is if this method is also viable: Calculate monthly logReturns ...
65 views

### Proof that we can price any derivative as the discounted value of its expected return under the risk neutral measure

I am reading a paper which tries to convey the intuition behind the Black-Scholes pricing formula. In that paper, the author states the following two things without proof, and I would like to know why ...
I have a optimization problem where the SDE is: $$dX(t) = [X(t)(u(t)-\beta(t))+\theta(t)]dt+X(t)u(t)\sigma dW(t), t \in [0,T], X(0) = X_0$$ where $\beta(t)$ and $\theta(t)$ are deterministic ...