We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Levy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples...

We prove asymptotic convergence results for some analytical expansions of solutions of degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori...

We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the 'implied Sharpe...

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{\o}lna (2011, CUP) analyzes models in which the...