ИСТИНА

This paper studies the hitting time problem for time-dependent diffusion processes involving the crossing of single and double barriers, where the boundaries may be time-dependent. The approach is based on the local time-space formula and a Markov chain approximation of the transition density function. We also study the case of stochastic volatility models and stochastic barriers. The problem is examined in the context of financial applications. An algorithm is presented, together with numerical results.