Intertemporal Arbitrage and the Markov Valuation of Securities

This paper explores the intertemporal nature of arbitrage and its connection to Markov processes. We suppose that an economy is in one of a fixed set (symbol insert) of possible states at each date. Assuming that prices and dividends are described by functions of the state of the economy at each date and are intertemporally arbitrage free, we construct a corresponding Markov process under which the current market value of any security is the expected value of its future dividends, given the current state of the Markov process. An equilibrium example is worked out using z-transform analysis.