Arbitrage Pricing and Arrow- Debreu Securities in a Model with Savings

In this paper we augment the risky assets of the Arrow- Debreu model, by adding a riskless asset (: akin to savings), whose price is one unit and which yields one unit of return in the next period from one unit of investment in the current period, irrespective of the state of nature that is realized. It turns out that arbitrage pricing of the assets is equivalent to the existence of Arrow- Debreu prices, which satisfy the no-arbitrage condition. Our primary result in this paper, is a theorem, which provides a sufficient condition under which there exist Arrow- Debreu prices satisfying the no-arbitrage condition and an additional condition, called “completeness”, of the asset market, under which such prices are unique