Let S00 = 1, S10 = 1, S20 = 2, and let B1, B2, B3 be three independent Brownian motions and consider the following three market models.

The filtration is always the one generated by all three Brownian motions.For each market, construct either an EMM or an arbitrage opportunity. Among those market models that are arbitrage-free, which are also complete?

For those markets which are (arbitrage-free and) incomplete, find a T-European claim which is not attainable. (Justify your arguments.)

Let S = 1, S = 1, S = 2, and let B!, B2, B be three independent Brownian motions. Denote by I := Si/Si (i = 1, 2) the discounted asset prices and consider the following three market models: d} = (2dt + dB/), (1) d} = $? (1dt + 2dB/), d1 = $}(3dt + dB; + dB), (2) d? = (-dt+dB; dB;), d= $}(dt + dB} +dB} dB;), (3) d} = ?(5dt dB; + dB} +dB?). The filtration is always the one generated by all three Brownian motions. For each market, construct either an EMM or an arbitrage opportunity. Among those market models that are arbitrage-free, which are also complete? For those markets which are (arbitrage-free and) incomplete, find a T-European claim which is not attainable. (Justify your arguments.) Let S = 1, S = 1, S = 2, and let B!, B2, B be three independent Brownian motions. Denote by I := Si/Si (i = 1, 2) the discounted asset prices and consider the following three market models: d} = (2dt + dB/), (1) d} = $? (1dt + 2dB/), d1 = $}(3dt + dB; + dB), (2) d? = (-dt+dB; dB;), d= $}(dt + dB} +dB} dB;), (3) d} = ?(5dt dB; + dB} +dB?). The filtration is always the one generated by all three Brownian motions. For each market, construct either an EMM or an arbitrage opportunity. Among those market models that are arbitrage-free, which are also complete? For those markets which are (arbitrage-free and) incomplete, find a T-European claim which is not attainable. (Justify your arguments.)