SFB 303 Discussion Paper No. B - 255

Author: Werner, Jan
Title: Arbitrage, Bubbles, and Valuation
Abstract: One of the important implications of the condition of the absence of arbitrage in asset markets is the "valuation principle". It asserts the existence of a strictly positive, continuous, linear operator assigning to the payoff of an asset, or the payoff of a portfolio of assets, its price. The operator extends valuation to claims which need not be payoffs of portfolios. It has various representations including martingale representation, and the present value pricing rule in terms of state prices. We examine the validity of the valuation principle in infinite asset markets. We consider an example of an economy with infinitely many states of nature. Assets are Arrow securities for every state, and a riskless security. The price of the riskless security is not equal to the infinite sum of prices of Arrow securities. This apparent "mispricing" indicates the failure of the present value pricing rule in terms of state prices. It does not, however, lead to an arbitrage opportunity. Moreover, portfolio demand of a risk neutral investor is well-defined. Although the valuation in terms of state prices does not hold, there is a valuation relationship which involves a pricing bubble for the riskless security.
Keywords: Arbitrage, Bubbles, Valuation, Asset market, Theory of financial markets
Creation-Date: June 1993
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