2) There are four possible states of the world: 1, 2, 3, and 4, with corresponding state claims: S1, S2, S3, and S4. Three assets are available with asset prices (in dollars) and payoffs (in "corn") in the four states given below: A1: price - $24 payoffs: (1, 2, 3, 4) A2: price = $13 payoffs: (0, 1, 2, 3) A3: price = $12 payoffs: (0, 0, 2, 4) No other assets are available. A) Find a portfolio that replicates the state claim S1 with payoff (1, 0, 0, 0) B) What is the price of that state claim? C) Explain why at least one of S2, S3, and/or S4 cannot be replicated with these assets.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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2) There are four possible states of the world: 1, 2, 3, and 4, with corresponding state
claims: S1, S2, S3, and S4. Three assets are available with asset prices (in dollars) and
payoffs (in "corn") in the four states given below:
A1: price
-
$24 payoffs: (1, 2, 3, 4)
A2: price
=
$13 payoffs: (0, 1, 2, 3)
A3: price = $12 payoffs: (0, 0, 2, 4)
No other assets are available.
A) Find a portfolio that replicates the state claim S1 with payoff (1, 0, 0, 0)
B) What is the price of that state claim?
C) Explain why at least one of S2, S3, and/or S4 cannot be replicated with these assets.
Transcribed Image Text:2) There are four possible states of the world: 1, 2, 3, and 4, with corresponding state claims: S1, S2, S3, and S4. Three assets are available with asset prices (in dollars) and payoffs (in "corn") in the four states given below: A1: price - $24 payoffs: (1, 2, 3, 4) A2: price = $13 payoffs: (0, 1, 2, 3) A3: price = $12 payoffs: (0, 0, 2, 4) No other assets are available. A) Find a portfolio that replicates the state claim S1 with payoff (1, 0, 0, 0) B) What is the price of that state claim? C) Explain why at least one of S2, S3, and/or S4 cannot be replicated with these assets.
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