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2 votes

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 ...
dm63's user avatar
  • 17.2k
2 votes

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 ...
Quasar's user avatar
  • 240
2 votes

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 ...
Achrbot's user avatar
  • 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 ...
Enrico Schumann's user avatar
1 vote

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{...
Kurt G.'s user avatar
  • 2,033
1 vote

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,...
Daneel Olivaw's user avatar
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_{...
Arshdeep's user avatar
  • 2,451

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