What's state price vector?

What is state price vector?.

Please explain me in detail is difficult to understand for me.

• Where did you hear of this, in what context? What is it that you don't understand? – SRKX Nov 25 '14 at 3:08
• What means the state price vector, and for that is used? – busterxD Nov 25 '14 at 3:11
• If S_0 is a price vector of N assets in the time zero. If D is a pairce matriz of N assets in n states. If Y is a vector in R^n strictly positive. Then S_0 = DY, why? – busterxD Nov 25 '14 at 3:36
• Please edit your question and provide all the details - using Latex - there. – Ric Dec 2 '14 at 9:51

Based on what I know for a leacture on Arrow Debrue Security assume that we live in a world with only 2 states and a Security $$S$$

• State 1 - Inflation > 1%
• State 2 - Inflation < 1%

And

• In State 1 security $$S$$ pays 1 i.e the payout fraction is 100%
• In State 2 security $$S$$ pays 0 i.e the payout fraction is 0%

This collection of states and Prices is called state price vector.

If you have more than one Security than you have a state price matrix.

States will such that sum of all payout fractions $$\Sigma_{i=1}^n P_i = 1$$. You can treat them as probilities. While pricing a security you can consider all state price vector for $$S$$ and find the price as $$PV(\Sigma_{i=1}^n P_i * S_i^{cf})$$ where $$S_i^{cf}$$ cashflow from security $$S$$ in state $$i$$.

I would recommend you read some papers on it

• Can you also give an interpretation of "state prices"? – emcor Nov 25 '14 at 13:09