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Oct
29
comment Change of measure discrete time
Agree that $\mathsf Q$ must satisfy $\mathsf E_\mathsf Q A_n = 0$ for all $n$, however I wondered which shape will the Radon-Nikodym density have in this case. Now, more than 2 years after OP was posted I think I can come up with the answer - in such a case I'll post it here. Regarding your comment on the uniqueness: indeed, one shall not expect it. Even if $A$ is 3-valued, you obtain a tree model where the market is not complete, so there are several martingale measures.
Oct
6
comment Why use leverage when it does not improve the risk/reward ratio?
What LTCM did in the beginning, was an arbitrage on bonds' spreads: each such trade would gain them only a little money even if they would invest all the money they had. They were sure though that such trades are profitable. Using leverage they were able to increase their exposure.
Sep
29
comment Why hold options when you can dynamically replicate their payoff?
Do I understand your point correctly here: in BS model the only risk is the directional one, and it can be completely eliminated by $\Delta$-hedging (in theory). Now, if we relax our assumptions a bit and still allow for continuous and cost-free $\Delta$-hedging, we are still exposed to volatility and interest-rate related risks (that are not assumed to be present in the BS model though) - right?
Sep
28
comment Basic question about bonds pricing
Very nice, I think that's the answer I was looking for.
Sep
28
accepted Basic question about bonds pricing
Sep
27
answered Monte Carlo Options Probability Calculation
Sep
27
comment Basic question about bonds pricing
I see your point: I just wondered what was the chicken and what was the egg in Hull's case.
Sep
27
comment Basic question about bonds pricing
Thanks Brian, just want to be sure I got you correctly. The price of more liquid bonds is mostly determined by supply/demand arguments, whereas for less liquid bonds one can do pricing based on more liquid issues: the latter can allow for the arbitrage in case the price of the former is inconsistent?
Sep
25
awarded  Citizen Patrol
Sep
25
comment How to test that a distribution has infinite mean?
+1 but I would suggest moving that to one of mathematical websites: MSE or MO. Perhaps, cross-validated also could be useful
Sep
25
asked Basic question about bonds pricing
Jul
4
comment Risk theory is a part of financial mathematics
That I understand - I meant only the mathematical part. Anyways, say the problem of ruin probabilities will not classically fall into financial mathematics?
Jul
4
answered Risk theory is a part of financial mathematics
Jul
4
comment Risk theory is a part of financial mathematics
Even in the wikipedia article, they seem to consider both pricing and risk management as subsets of financial mathematics. The discussion on P and Q is indeed interesting, thanks for pointing it out.
Jul
4
asked Risk theory is a part of financial mathematics
Jun
12
awarded  Popular Question
Jun
4
comment George Soros models
NP, I just updated my description recently so it might have not been there before
Jun
3
comment George Soros models
Well, I am familiar with principles of the stochastic optimal control and dynamic programming. Surely, you can incorporate the reflexivity there - my question was rather on how to incorporate it in a practically meaningful way, that's why I've whether there are some financial models known that involve reflexivity as per Soros.
Jun
3
comment Why does Black-Scholes equation hold on continuation region of American Option?
For the American option, the solution is given by a Optimal Stopping/Free-boundary Problem. Here you seem to have European vanilla one
Jun
1
comment George Soros models
That's indeed interesting, a very recent paper - thanks!