We derive semi-analytic solutions for power option prices under the Heston model; specifically, the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment. Unlike the majority of stochastic volatility models, there remains a significant problem...

The aim of this work is to obtain sufficient conditions for stability of multidimensional jump-diffusion processes in the sense of stability in distribution and stability at the equilibrium solution. The technique employed is to construct appropriate Lyapunov functions.

We prove uniform L2-convergence of local times of aperiodic recurrent random walks to local times of strictly [alpha]-stable processes with [alpha] > 1.