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Unformatted text preview: held a unit of each ordinary security. Let
, ,…, denote the s row vector of R (that is, the s state‐contingent payout). These ordinary securities are sold at Date 0, at prices , ,… . Let , ,…,
be a vector of the amount of each of these M ordinary securities bought or sold
by Agent i at Date 0 (that is,
problem is: is a portfolio of ordinary securities). The agent's Choose , to maximize subject to 1.
2.
3. 0 for each s Are complete Arrow securities and ordinary securities the same? The payoff
for a compete set of Arrow securities is
1
0
⋮
0 …0
⋮
1
⋮
…1 So, if payoff matrix R is of full rank, ⋅ ⁻¹
. This suggests that each
column element of ⁻¹ represent portfolio of ordinary securities that will
replicate an Arrow security that pays off 1 unit of purchasing power in state
and nothing else in any other state. An Example
Suppose there are 2 states and 2 ordinary securities. Security 1 pays off 6 units of
purchasing power in State 1 and 2 units of purchasing power in State 2: ₁
6,2 .
Security 2 pays off 4 units of purchasing power in State 1 and 10 units of
purchasing power in State 2: ₂
4,10 . In this case,
64
2 10
Not...
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 Winter '14
 Economics

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