In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses at a constant rate and earns random positive gains at random times. When the surplus is invested in a risky asset following a geometric Brownian...
Two numerical methods are presented that can be used to solve
second order nonlinear ordinary differential equations with periodic
boundary conditions. One of these methods is a shooting method developed
solely for the periodic problem. The other, "quasilinearization,"
is a method applicable to a wide variety of problems. It is...