  The study deals with the ruin problem when an insurance company having two
business branches, life insurance and non-life insurance, invests its reserve
into a risky asset with the price dynamics given by a geometric Brownian
motion. We prove a result on smoothness of the ruin probability as a function
of the initial capital and obtain for it an integro-differential equation
understood in the classical sense. For the case of exponentially distributed
jumps we show that the survival probability is a solution of an ordinary
differential equation of the 4th order. Asymptotic analysis of the latter leads
to the conclusion that the ruin probability decays to zero in the same way as
in the already studied cases of models with one-side jumps.
