Backward Stochastic PDEs Related to the Utility Maximization Problem

We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As examples the cases of power, exponential and logarithmic utilities are consideredBackward stochastic partial dierential equation, utility maximization problem, semimartingale, incomplete markets

The Adomian series representation of some quadratic BSDEs

The representation of the solution of some Backward Stochastic Differential Equation as an infinite series is obtained. Some exactly solvable examples are considered.Comment: 16 page

Linear dynamics of the solar convection zone: excitation of waves in unstably stratified shear flows

In this paper we report on the nonresonant conversion of convectively unstable linear gravity modes into acoustic oscillation modes in shear flows. The convectively unstable linear gravity modes can excite acoustic modes with similar wave-numbers. The frequencies of the excited oscillations may be qualitatively higher than the temporal variation scales of the source flow, while the frequency spectra of the generated oscillations should be intrinsically correlated to the velocity field of the source flow. We anticipate that this nonresonant phenomenon can significantly contribute to the production of sound waves in the solar convection zone.Comment: 8 pages. To appear in the proceedings of the conference "Waves in Dusty, Solar and Space Plasmas", Leuven, Belgium 21-26 May 200