# Tag Info

Accepted

### Expected value and Variance of a stopped random process

Although Math SE might be a bit more suited for this one, I wanted to give it a try. The answer relies on the law of total expectation, the law of total variance, and the relationship between Euler's ...
• 6,772
Accepted

### Figure of Stopping and Continuation Region

The exercise boundary $B_t$ for a finite maturity American put option is not a constant function of time as in your plot. As mentioned in the excerpt, $B_T = K$ at maturity. But for $t < T$, we ...
• 6,064
Accepted

### Why do we need to split market and default information into 2 separate filtrations?

I think you are absolutely correct if the hazard rate is deterministic, although I think you are forgetting a discounting factor in your example. But sometimes the hazard rate cannot be assumed to be ...
• 845

• 2,432
1 vote
Accepted

### Probability that return exceeds a certain level before a certain time (Black-Scholes)

In that case, the problem becomes a non-trivial stopping time problem. Consider a filtered probability space $(\Omega, \mathcal{F}, \mathbb{P})$ equipped with the natural filtration of a standard ...
• 14.7k

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