# Tag Info

### Why A Derivative With Intrinsic Arbitrage Cannot Be Valued & Hedged With Assets In Risk Neutral?

Valuing something to the writer vs valuing it to the buyer makes no difference. We just value the instrument. In this case the buyer surely would prevent the writer from collecting the fee, by ...
• 17.2k
Accepted

### Conditional expectation of increments of stochastic process

Since the process has independent increments, the increment $X_t - X_s$ is independent of $X_s - X_0$. So, your estimate of $X_t - X_s$, based on information learned by observing the process upto time ...
• 240
Accepted

### How to prove that a market is incomplete using the concept of EMMs?

Regarding your first problem, you are correct that constructing two different EMM's is sufficient to show that the market is incomplete. For a candidate measure $\mathbb{Q}$ to be an EMM, we require ...
• 373
1 vote

### Is this arbitrage? Infinite payoff / infinite loss (energy generation investment problem)

Arbitrage means that you can a profit (in at least some states of the world), without the risk of losing. IIUC, in your state 2, you'd make a loss, and the bigger your investment x, the bigger the ...
• 3,501
1 vote
Accepted

### Black Scholes/American Put/Martingale Condition

Too long for a comment. \begin{align} S_t&=S_0\,e^{rt+\sigma W_t-\sigma^2t/2}\,,&S_t^{-\alpha}=S_0^{-\alpha}\,e^{-\alpha\, r\,t\,-\,\alpha\,\sigma\, W_t\,+\,\alpha\,\sigma^2\,t/2}\,, \end{...
• 2,033
1 vote
Accepted

### Geometric Brownian motion and semi-martingality

I will provide a heuristic explanation. A local martingale $(M_t)_t$ (mart) is a stochastic process whose expected increments are zero that is $E(\mathrm{d}M_t)=0$. Under suitable technical conditions,...
• 8,119
1 vote

### Martingale under risk neutral probability

You already have it. Risk neutral measure is one where tosses are still independent but each individual toss has probability of 0.5 up or down. Say you're at step n, with $S_{n}$ known. \$E(S_{n+1}|F_{...
• 2,451

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