The kinetic and interaction energies of a trapped Bose gas: Beyond the mean field

The kinetic and interaction energies of a three-dimensional dilute ground-state Bose gas confined in a trap are calculated beyond a mean-field treatment. They are found to depend on the pairwise interaction trough two characteristic lengths: the first, a, is the well-known scattering length and the second, b, is related to the latter by b=a-\lambda d a/d\lambda with \lambda being the coupling constant. Numerical estimations show that the pairwise interaction energy of a dilute gas of alkali atoms in a trap is negative (in spite of the positive scattering length); its absolute value is found by about the order of magnitude larger than that of the mean-field interaction energy that corresponds to the last term in the Gross-Pitaevskii functional.Comment: 5 pages, REVTeX, 1 figure inserte

Pricing and hedging in incomplete markets with coherent risk

We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coherent risk measures and equilibrium considerations. Furthermore, we propose a way to apply the above technique to the coherent estimation of the Greeks

Credit default swaps and their market function

Credit derivative instruments allow default risk to be segregated from debt of all kinds. They have granted investors the ability to hedge their portfolios and provided numerous institutions with a new source of income. However, the market for credit default swaps is neither transparent nor regulated, perhaps undermining the stability of the financial system it has helped innovate.Credit derivatives ; Swaps (Finance)

Reforming the over-the-counter derivatives market: what’s to be gained?

While derivative financial instruments have made the hedging and exchange of risk more efficient, the recent crisis showed that they also pose a substantial threat to financial stability in times of systemic turmoil. Underlying much of this threat is the lack of transparent reporting in the over-the-counter market for these instruments. This Commentary discusses the advantages of one solution to the transparency proble: moving the settlement or trading of derivatives to exchanges or clearinghouses.Derivative securities ; Financial market regulatory reform ; Over-the-counter markets