A new proposition on the martingale representation theorem and on the approximate hedging of contingent claim in mean-variance criterion

In this work we revisit the problem of the hedging of contingent claim using mean-square criterion. We prove that in incomplete market, some probability measure can be identified so that becomes -martingale under .This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure.

An Afriat theorem for the collective model of household consumption

We provide a nonparametric 'revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a ‘collective’ version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.

Exercise elicits phase shifts and acute alterations of melatonin that vary with circadian phase

To examine the immediate phase-shifting effects of high-intensity exercise of a practical duration (1 h) on human circadian phase, five groups of healthy men 20-30 yr of age participated in studies involving no exercise or exposure to morning, afternoon, evening, or nocturnal exercise. Except during scheduled sleep/dark and exercise periods, subjects remained under modified constant routine conditions allowing a sleep period and including constant posture, knowledge of clock time, and exposure to dim light intensities averaging (±SD) 42 ± 19 lx. The nocturnal onset of plasma melatonin secretion was used as a marker of circadian phase. A phase response curve was used to summarize the phase-shifting effects of exercise as a function of the timing of exercise. A significant effect of time of day on circadian phase shifts was observed (P < 0.004). Over the interval from the melatonin onset before exercise to the first onset after exercise, circadian phase was significantly advanced in the evening exercise group by 30 ± 15 min (SE) compared with the phase delays observed in the no-exercise group (-25 ± 14 min, P < 0.05). Phase shifts in response to evening exercise exposure were attenuated on the second day after exercise exposure and no longer significantly different from phase shifts observed in the absence of exercise. Unanticipated transient elevations of melatonin levels were observed in response to nocturnal exercise and in some evening exercise subjects. Taken together with the results from previous studies in humans and diurnal rodents, the current results suggest that 1) a longer duration of exercise exposure and/or repeated daily exposure to exercise may be necessary for reliable phase-shifting of the human circadian system and that 2) early evening exercise of high intensity may induce phase advances relevant for nonphotic entrainment of the human circadian system.