The no-trade interval of Dow and Werlang: Some clarifications

Abstract

ED EPSInternational audienceThe aim of this paper is two-fold: first, to emphasize that the seminal result of Dow and Werlang (1992) remains valid under weaker conditions, and this even if non-positive prices are considered, or equally that the no-trade interval result is robust when considering assets which can yield non-positive outcomes. Second, to make precise the weak uncertainty aversion behavior characteristic of the existence of such an interval

Mean-risk analysis with enhanced behavioral content

“…If the price is lower than the lower bound of the interval, the individual buys; if the price is higher than the upper bound, he/she short sells; for prices within the interval, he/she declines holding a position. This result, intuitively plausible and compatible with observed investment behavior, is further extended by Chateauneuf and Ventura (2010). 4 COROLLARY 4.…”

“…The M-Δ model bridges these two situations. Chateauneuf and Ventura (2010) show that Dow and Werlang's (1992) result holds for nonpositive assets. Note that, owing to translation invariance, no assumptions were necessary about the sign of X in the M-Δ analysis above.…”

Market Allocations under Ambiguity: A Survey

“…As a result, there is an interval of prices at which it is optimal not to go short nor long, leading to portfolio inertia: at the zero position, the optimal portfolio (i.e., holding zero uncertain assets) is not responsive to price changes as long as they remain within the interval identied. Chateauneuf and Ventura (2010) extend Dow and Werlang's original result within the CEU model, showing it holds with possibly negative outcomes and under a weaker condition than convexity of the capacity. Higashi et al (2008) explore further this inertia property without assuming a particular decision model, and give an axiomatic foundation for the "kink at certainty" property that underlies portfolio inertia.…”

Endogenous incompleteness of financial markets: The role of ambiguity and ambiguity aversion

“…Unlike in the case of subjective expected utility, there is no single price at which to switch from buying to selling. As recently discussed by Chateauneuf and Ventura (2008), these findings remain valid also when non-positive prices and assets possibly yielding a non-positive payoff are considered. Further, the no-trade interval result still holds when convexity of the capacity is weakened to super-additivity at certainty, that corresponds to aversion to some specific increases of uncertainty.…”