跳躍拡散過程での取り替えモデル

概要

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Replacement investment decision under uncertain maintenance and operation cost is discussed in several recent papers, in which uncertainty is described using geometric Brownian motion. In order to take sudden increasing of maintenance and operation cost caused by unpredictable accidents and disasters into consideration, in this paper we concern to use jump diffusion process with n positive jumps. Occurrence of each jump is assumed driven by a Poisson process. Size of jumps are random variables, the probability distribution is assumed to be exponential distribution and Erlang distribution. We derive equations for solving the optimal level of maintenance and operation cost for replacement, and show explicit formulas for expected present value of total cost and expected replacement period. For the purpose of considering the situations that maintenance and operation cost increase discretely, we use a pure jump process that the geometric Brownian motion part is eliminated from the jump diffusion process. In this case, we find that the smooth pasting condition is not contained in the equations for solving the optimal level for replacement. Numerical results show that unpredictable events increase the optimal level for replacement and total cost, but decrease expected replacement period. We also examine the effects of probability distributions of jump size.