As published, the proposed amendment used the terms property and asset(s) interchangeably.
Relative measurements between a spacecraft placed in an EML-2 halo orbit and lunar surface asset(s) are simulated and processed.
Alternatively stated, we would say that the asset S is a ({mathcal {P}} -bubble if it is a (mathbb {P}} -bubblefor every (mathbb {Q}if {mathcal {P}}).
Consider a risky asset S such that there exists a ({mathbb {Q}}^{tilde {alpha }}in {mathcal {P}}_{S}) for which the asset is a strict ({mathbb {Q}}^{tilde {alpha }} -local martingale.
where Bi,b specifies the interest paid to the lender by the hedger who borrows cash and pledges the risky asset S i as collateral, and the constant hi,b represents the haircut for the ith asset pledged.
For instance, the payoff (H=left (frac {1}{N} sum _{n=1}^{N}S^{1}_{t_{n}}-Kright)^) of an average-price Asian call option on the first asset, S 1, can be approximated by a call option based on a continuous-time average of asset prices, (Happrox left (frac {1}{T}{int _{0}^{T}}{S^{1}_{t}},dt-Kright)^).
If we assume that the proceeds from short selling of the risky asset S i can be used by the hedger (this is typically not true in practice), we also set (psi ^{i,l}_{t}=0) for all t∈[0,T], and thus the process Bi,l becomes irrelevant as well.
Hence by the long cash position (resp. short cash position), we mean the situation when (xi ^{i}_{t} S^{i}_{t} leq 0 left (text {resp}. xi ^{i}_{t} S^{i}_{t} geq 0right)), where (xi ^{i}_{t}) is the number of hedger's positions in the risky asset S i at time t.
Hence, (mathcal {P}^{text {ngd}}(Q^{P,theta })) is the set of a-priori valuation measures equivalent to Q P,θ, which satisfy the no-good-deal restriction under Q P,θ but might not be local martingale measures for the stock price process S (yet they are w.r.t. the market with only the riskless asset S 0≡1).
This issue does not appear in the less general setting of Section "Uncertainty solely about the volatility" where, thanks to the zero drift assumption b=0 for the traded asset S, the expression for (widehat {F}(widehat {a}^{1/2}Z)) greatly simplifies to (42) and this allows by direct comparison to obtain (overline {a}) as the corresponding worst-case volatility.
As a simple example of cash flows, consider the situation where the hedger sells at time t the European call option on the risky asset S i. Then m=1, t1=T, and the terminal payoff from the perspective of the hedger equals (a_{1}=- left (S^{i}_{T}-Kright)^).
