Equivalent Martingale Measure and Market Completeness

[quotes]

Hi guys, I recently read about numeraire changing in Martingale Pricing technique. I heard the "Equivalent Martingale Martingale" dresses this issue and set a standard on whether there is a no-arbitrage price as the probabilistic expectation, called "Market Completeness".

So do you have any ideas about the theories above? Thanks in advance.

 

[diegosanaz]

Yeah, this is the thing:

1. If there exist an Equivalent Martingale Measure such that the discounted present value of an asset is equal to the spot price, then there is no arbitrage price (First Fundamental Theorem of Asset Pricing).

2. If there is only one Equivalent Martingale Measure, then the market is said to be complete (Second Fundamental Theorem of Asset Pricing).

 

[quotes]

Yeah, this is the thing:

1. If there exist an Equivalent Martingale Measure such that the discounted present value of an asset is equal to the spot price, then there is no arbitrage price (First Fundamental Theorem of Asset Pricing).

2. If there is only one Equivalent Martingale Measure, then the market is said to be complete (Second Fundamental Theorem of Asset Pricing).

where did you see them?

 

[diegosanaz]

Shreve Stoch Calculus for Finance II. Pages 231 and 232

 

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Shreve Stoch Calculus for Finance II. Pages 231 and 232

Many thanks.

 

[DailyStockSelect]

hemmm when i see martingale, i run away!

 

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Well I guess I have not made the question clear.
The traditional argument equates a risk-neutral measure to an equivalent martingale measure (EMM).
But I doubt if a debt or bond asset is unnecessary in construction of equivalent martingale measure.
Traditional arguments require at least one asset to be deterministic where as other assets stochastic, like a bond and a stock.
But I wonder if EMM still holds when all of assets are stochastic?