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ty: – When a=c, – We got 11 0011[ ] v a r ( ) [ ] cciii i c cRRR R Crr ??? ?? ? ? ???0 0 0 0( ) ( )ccaa c a cccR R R R R R R? ??? ? ? ? ? ?Asset market ? Complete market: – An asset a valued Vas in state s, how much is this asset worth in period 0? – Construct a portfolio: holding Vas unit ArrowDebreu Security s, means a AD security valued $1 while the portfolio valued Vas in state s. so: 1Sa s a ssp p V?? ?Asset market ? Complete market: – Let be the probability of s – it’s the value of a portfolio that pays off $1 for certain, and R0 be the riskfree return of it. Then: 1( ) c o v ( , )Ssa a s s a a as sp p p pp V E V V E E V?? ? ? ??? ? ? ??11SSssssssppEp??? ??????s?01pER? ?Asset market ? Complete market: 0c o v ( , )aaaV ppVR ???Asset market ? Pure arbitrage: – No opportunity for pure arbitrage. – No arbitrage principle: if then – There exist price such that the value of any asset a is given by: – Let we have: 0?VX 0?pX1( , )S??1Sa s a sspV??? ?/ssZ ???0000c ov ( , ) c ov ( , )c ov ( , )aaa a aaaVVp Z V Z V R R ZppR R R Z R? ? ? ? ?? ? ?Assignment ? Textbook:。Lecture 9: time and assets market Contents ? Intertemporal prefer