Lecture 10

These ordinary securities are sold at date 0 at

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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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