1.consider a market with four securities and three possible states of the world. the asset returns' matrix is given by:
      1  3  1.5   2
R    1  2  0.5  1  
      1  1    0    0
the asset price vector is given by Q=[1  2  0.6  1]. are there ant arbitrage opportunities in this market?

2.andy and kim live together.andy may invest $10000 in kim's education this year. in present value terms,this investment will raise kim's future earning by $24000.if they stay together,they will share the benefit from the additional earning .however .there is a 50% chance that they will split up in the future.if they were married (or in a civil partnership) and then split,andy would get half of kim's additional earning.if they were living together without any legal ties and then they split,then andy would get nothing .andy is risk neutral.

will andy invest in kim's education? does your answer depend on the couple's legal status?


谢谢各位~