An exponential estimate of ruin probability for an insurance company which invests all its capital in risk assets is found. The process which describes the risky assets is assumed to follow a geometrical Brownian motion. ...

The existence and uniqueness of solution of stochastic differential equation driven by standard Brownian motion and fractional Brownian motion with Hurst parameter H belongs (3/4, 1) is established.

We give a sufficient condition on coefficients of a nonhomogeneous stochastic differential equation with non-Lipschitz diffusion for a solution starting from arbitrary nonrandom positive point to stay positive. Some examples ...