ScholarWorks@숙명여자대학교

초록

In this paper, a surplus process with investments is introduced. Whenever the level of the surplus reaches a target value V > 0, amount S(0 ≤ S ≤ V) is invested into other business. After assigning three costs to the surplus process, a reward per unit amount of the investment, a penalty of the surplus being empty and the keeping (opportunity) cost per unit amount of the surplus per unit time, we obtain the long-run average cost per unit time to manage the surplus. We prove that there exists a unique value of S minimizing the long-run average cost per unit time for a given value of V , and also that there exists a unique value of V minimizing the long-run average cost per unit time for a given value of S. These two facts show that an optimal investment policy of the surplus exists when we manage the surplus in the long-run.

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