ALL PARTS PLEASE

1. For the following parts you need to provide full rigorous proofs for full credit. (a) (1 point) Show that any 2 by 2 market with one risky asset and one riskless asset is complete. (b) (1 point) Show that any 3 by 2 market with one risky and one riskless asset is incomplete. (c) (2 point) In the special case of a 2 by 2 market with one risky and one riskless asset, prove that AF (arbitrage free) implies there is a risk neutral martingale probability Q 1. For the following parts you need to provide full rigorous proofs for full credit. (a) (1 point) Show that any 2 by 2 market with one risky asset and one riskless asset is complete. (b) (1 point) Show that any 3 by 2 market with one risky and one riskless asset is incomplete. (c) (2 point) In the special case of a 2 by 2 market with one risky and one riskless asset, prove that AF (arbitrage free) implies there is a risk neutral martingale probability