The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme

Deterministic Approximation for Stochastic Control Problems

We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise "intensity" is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem is asymptotically optimal for the stochastic problems. Key Words : Stochastic and deterministic control, Stochastic differential equations, Weak convergence, Asymptotic optimality. AMS Subject Classification: 93E20, 93C15, 60B10, 60F17, 60G44, 49J15, 49K40, 49M45 Acknowledgement : This work was partially supported by GNAFA / CNR of the Italian National Research Council allowing a visit of the first and last authors at the University of Padova. The work of the last author was also supported by National Science Foundation Grant DMS 9301200 and NATO Scientific Exchange Grant CRG 900147 1.Introducti..