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Answers for “为什么状态价格 $\psi_j$ 不是概率,而转换后的向量 $q_j$ 是?”

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You convert a state price vector into risk-neutral probabilities by multiplying each state price by the gross risk-free factor (1+i)(1+i), where ii is the per-period risk-free interest rate. This scaling transforms the monetary prices of Arrow-Debreu securities into a valid probability distribution that sums to 1.

Conditions: The state prices ψj\psi_j are already determined.; ii is the known per-period risk-free interest rate.; The market is a one-period finite-state model.