Decreasing supply to increase price is not impossible, though it is a very delicate matter. I see the following options for decreasing supply:

a) impose demurrage rate on the stabilized asset as in freicoin; (as a grossly inferior substitute txn fees could be used instead)
          i) reissue demurred assets when price is constant (e.g. as mining reward or distribution to someone besides the asset holder)
          ii) destroy demurred assets when price is falling
b) maintain an escrow fund that purchases assets at a fixed exchange rate; the fund is always open to purchase assets until the escrowed funds are exhausted.
c) a mixture of (a) and (b); escrowed coins are returned to the initial asset issuer as demurrage occurs (for the issuer demurrage is interest)

Thezerg's comment is on point here. I am also concerned about the mechanism that rewards asset issuers for creating assets and backing them with escrow funds. Asset issuers need to get a positive risk-adjusted return on their escrowed capital. Demurrage fees could potentially fund this. It is not going to be sufficient to back assets one-to-one. Not with the value of the backing halving and doubling in value from month to month. You will need something like 3 to one backing to be credible. What motivates asset issuers to sink 3 USD worth of BTC into the creation of 1 USD worth of cryptoasset. It's going to have to be demurrage. i.e. the asset has to gradually melt returning its collateral to the asset issuer in the process.

As much as it pains me to give evoorhess credit for anything, he is 99% on point here. Let's go over how a speculative attack works and why it guarantees devaluation of the derivative when its backing falls below parity under certain assumptions (the 1% where evoorhees goes wrong is his failure to state the qualifying assumption (b) [if (b) does not hold, a speculative attack becomes impossible])

Assumptions:
a) I assume that the mastercoinUSD derivative is initially trading at parity. (plan is to demonstrate that this assumption is inconsistent with assumptions 2 and 3)
b) I also assume that the escrow fund is insufficient to back the mastercoinUSD derivative on a one-to-one basis. (fractional reserve)
c) I assume that the attacker can get collateral sufficient to borrow a significant fraction of all existing mastercoinUSD derivatives. He will tempt people into this by offering to pay very high interest rates on the loan.

Executing the attack:
1) The attacker borrows mastercoinUSD derivatives, offering a high rate of interest to anyone who is willing to lend them. If the lenders actually expect (a) to hold in the future, then they should be delighted to accept the high rate of return. If not, then they should be selling mastercoinUSD now and thus assumption (a) could not hold.

2) The attacker now controls a bunch of mastercoinUSD and can exchange them using the escrow fund. He does this, depleting the escrow fund in the process. Other people observe what is going on and start joining the attack either by selling on the market or using the escrow fund to sell. Their participation helps a lot, but is not essential for this to work. In the process, the attackers accumulate the escrowed assets. These will end up as pure attacker profit. The attack continues until the escrow fund is completely exhausted. Exhaustion is possible due to assumption (b).

3) The mastercoinUSD is now unbacked. It is completely worthless paper trading for pennies on the dollar if we were hoping for an IMF bailout and $0.00 under the harder realities of cryptocurrency markets.

4) The attacker's work is done. He purchase up the valueless mastercoinUSD and pay back his mastercoinUSD creditors worthless paper. The hapless holders of mastercoinUSD suffer a total loss.

The key takeaway here is that a 1-to-1 reserve is never going to be credible. Any loss in value of collateral will set off the attack process. The derivative's price will collapse to zero even under a quite small adverse market fluctuation. Suppose we have a 100-to-1 reserve, however. A speculative attack can never happen in this case except under the most extreme circumstances (e.g. the price of collateral falls 100-fold relative to the USD). The problem then becomes how do we get people to spend 100 USD of coin to create an asset which they then sell for 1 USD. It is a thorny problem, but not impossible as evoorhees implies.