Option Pricing from Path Integral for Non-Gaussian Fluctuations. Natural Martingale and Application to Truncated L\'evy Distributions

Within a path integral formalism for non-Gaussian price fluctuations we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is evaluated for truncated L\'evy distributions.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html. Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/33

Gamma-Ray Burst Phenomenon as Collapse of QED Magnetized Vacuum Bubble: Analogy with Sonoluminescence

We consider the phenomenon of a gamma-ray burst as a nonlinear collapse of a magnetic cavity surrounding a neutron star with very strong magnetic field B = 10^15 - 10^16 G due to the process of the bubble shape instability in a resonant MHD field of the accreting plasma. The QED effect of vacuum polarizability by the strong magnetic field is taken into account. We develop an analogy with the phenomenon of sonoluminescence (SL) when the gas bubble is located in the surrounding liquid with a driven sound intensity. We show that this analogy between GRB and SL phenomena really exists.Comment: 14 pages, submitted to Natur