arXiv subjects
Publications and source records attributed to Viktor Antipov.
This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability for large initial capital values is investigated.
The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric Lévy process. Considering the ruin probability as a of the capital reserve we obtain for it a partial integro-differential equation understood in a viscosity sense and prove a result on the uniqueness of the viscosity solution for a corresponding boundary value problem.
The paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing a random variations in the economic and financial environments. We prove smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation.