Abstract not found

This paper presents a resolution of the paradox proposed by the example of an economy with complete markets and a multiplicity of martingale measures constructed by Artzner and Heath (1995). The resolution lies in noting that completeness is with respect to a topology on the space of cash flows and is connected with uniqueness of the price functional in the topological dual space. Uniqueness may be lost outside the dual and this is what occurs in the counterexample of Artzner and Heath.

We take another look at the Chu construction and show how to simplify it by looking at

In an incomplete market the price of a claim f in general cannot be uniquely identified by no arbitrage arguments. However, the “classical” super replication price is a sensible indicator of the (maximum selling) value of the claim. When f satisfies certain pointwise conditions (e.g., f is bounded from below), the super replication price is equal to sup Q EQ[f], where Q varies on the whole set of pricing measures. Unfortunately, this price is often too high: a typical situation is here discussed in the examples. We thus define the less expensive weak super replication price and we relax the requirements on f by asking just for “enough ” integrability conditions. By building up a proper duality theory, we show its economic meaning and its relation with the investor’s preferences. Indeed, it turns out that the weak super replication price of f coincides with sup Q∈MΦ EQ[f], where MΦ is the class of pricing measures with finite generalized entropy (i.e., E[Φ ( dQ)] <∞) and where Φ is the convex dP conjugate of the utility function of the investor. 1. Introduction. We

This paper reevaluates the mathematical and economic meaning of no arbitrage in frictionless markets. Contrary to the traditional view, no arbitrage is not generally equivalent to the existence of an equivalent martingale measure. Departures from this equivalence allow asset prices to contain a monetary component. The refined view is that no arbitrage and no private monetary value components are equivalent to the existence of an equivalent martingale measure. The implications of prices having a monetary value component for option pricing are discussed.