Optimal control of the surplus in an insurance policy

A classical continuous time surplus process is modified by adding two actions If the level of the surplus goes below tau >= 0 we increase the level of the surplus up to initial level u > tau by injecting capital to the surplus Meanwhile the excess amount of the surplus over V > u is invested continuously to other business After assigning several costs related to managing the surplus we obtain the long-run average cost per unit time and illustrate a numerical example to show how to find an optimal investment policy minimizing the cost (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved