Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-diffusion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behav...