Arbitrage-Free Pricing Before and Beyond Probabilities

"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We give examples of such cases. We also show that arbitrage freedom is equivalent to the continuity of the pricing linear form in the relevant topology. Finally we analyze the possible loss of martingality of asset prices with lognormal stochastic volatility. For positive correlation martingality is lost when the financial process is modelled through standard probability theory. We show how to recover martingality using the appropriate mathematical tools.Comment: 5 page

Selfduality of d=2 Reduction of Gravity Coupled to a Sigma-Model

Dimensional reduction in two dimensions of gravity in higher dimension, or more generally of d=3 gravity coupled to a sigma-model on a symmetric space, is known to possess an infinite number of symmetries. We show that such a bidimensional model can be embedded in a covariant way into a sigma-model on an infinite symmetric space, built on the semidirect product of an affine group by the Witt group. The finite theory is the solution of a covariant selfduality constraint on the infinite model. It has therefore the symmetries of the infinite symmetric space. (We give explicit transformations of the gauge algebra.) The usual physical fields are recovered in a triangular gauge, in which the equations take the form of the usual linear systems which exhibit the integrable structure of the models. Moreover, we derive the constraint equation for the conformal factor, which is associated to the central term of the affine group involved.Comment: 7 page

Impact of the isoprene photochemical cascade on tropical ozone

Tropical tropospheric ozone affects Earth's radiative forcing and the oxidative capacity of the atmosphere. Considerable work has been devoted to the study of the processes controlling its budget. Yet, large discrepancies between simulated and observed tropical tropospheric ozone remain. Here, we characterize some of the mechanisms by which the photochemistry of isoprene impacts the budget of tropical ozone. At the regional scale, we use forward sensitivity simulation to explore the sensitivity to the representation of isoprene nitrates. We find that isoprene nitrates can account for up to 70% of the local NO_x = NO+NO_2 sink. The resulting modulation of ozone can be well characterized by their net modulation of NO_x. We use adjoint sensitivity simulations to demonstrate that the oxidation of isoprene can affect ozone outside of continental regions through the transport of NO_x over near-shore regions (e.g., South Atlantic) and the oxidation of isoprene outside of the boundary layer far from its emissions regions. The latter mechanism is promoted by the simulated low boundary-layer oxidative conditions. In our simulation, ~20% of the isoprene is oxidized above the boundary layer in the tropics. Changes in the interplay between regional and global effect are discussed in light of the forecasted increase in anthropogenic emissions in tropical regions

Cosmological billiards and oxidation

We show how the properties of the cosmological billiards provide useful information (spacetime dimension and $p$-form spectrum) on the oxidation endpoint of the oxidation sequence of gravitational theories. We compare this approach to the other available methods: $GL(n,R)$ subgroups and the superalgebras of dualities.Comment: To appear in the Proceedings of the 27th Johns Hopkins Workshop and in the Proceedings of the 36th International Symposium Ahrenshoop; v2: minor error correcte

Isoprene photooxidation : new insights into the production of acids and organic nitrates

We describe a nearly explicit chemical mechanism for isoprene photooxidation guided by chamber studies that include time-resolved observation of an extensive suite of volatile compounds. We provide new constraints on the chemistry of the poorly-understood isoprene δ-hydroxy channels, which account for more than one third of the total isoprene carbon flux and a larger fraction of the nitrate yields. We show that the cis branch dominates the chemistry of the δ-hydroxy channel with less than 5% of the carbon following the trans branch. The modelled yield of isoprene nitrates is 12±3% with a large difference between the δ and β branches. The oxidation of these nitrates releases about 50% of the NOx. Methacrolein nitrates (modelled yield ≃15±3% from methacrolein) and methylvinylketone nitrates (modelled yield ≃11±3% yield from methylvinylketone) are also observed. Propanone nitrate, produced with a yield of 1% from isoprene, appears to be the longest-lived nitrate formed in the total oxidation of isoprene. We find a large molar yield of formic acid and suggest a novel mechanism leading to its formation from the organic nitrates. Finally, the most important features of this mechanism are summarized in a condensed scheme appropriate for use in global chemical transport models

Global oceanic emission of ammonia: constraints from seawater and atmospheric observations

Current global inventories of ammonia emissions identify the ocean as the largest natural source. This source depends on seawater pH, temperature, and the concentration of total seawater ammonia (NHx(sw)), which reflects a balance between remineralization of organic matter, uptake by plankton, and nitrification. Here we compare [NHx(sw)] from two global ocean biogeochemical models (BEC and COBALT) against extensive ocean observations. Simulated [NHx(sw)] are generally biased high. Improved simulation can be achieved in COBALT by increasing the plankton affinity for NHx within observed ranges. The resulting global ocean emissions is 2.5 TgN a−1, much lower than current literature values (7–23 TgN a−1), including the widely used Global Emissions InitiAtive (GEIA) inventory (8 TgN a−1). Such a weak ocean source implies that continental sources contribute more than half of atmospheric NHx over most of the ocean in the Northern Hemisphere. Ammonia emitted from oceanic sources is insufficient to neutralize sulfate aerosol acidity, consistent with observations. There is evidence over the Equatorial Pacific for a missing source of atmospheric ammonia that could be due to photolysis of marine organic nitrogen at the ocean surface or in the atmosphere. Accommodating this possible missing source yields a global ocean emission of ammonia in the range 2–5 TgN a−1, comparable in magnitude to other natural sources from open fires and soils