유전알고리즘을 활용한 최적 분할연금 설계
Genetic Algorithm Approaches to Optimal Pension Payout Planning
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초록
본 논문은 프로그램 인출펀드의 설계방안을 제시함으로써 은퇴자들에게 다양한 분배기간 상품을 제공하는데 그 목적이 있다. 이를 위해 우리는 기대소비효용과 기대상속효용 등 기대생애효용을 극대화하는 인출비율을 제시하였다. 이러한 최적화문제를 다기간 비선형 모형으로 구축하였으며, 유전알고리즘 방법론을 활용하여 수치적 최적인출비율을 제시하였다. 분석결과 첫째, 최적인출비율은 가입초기에 10% 수준을 유지하다가 연령이 증가함에 따라 점차 증가하는 것으로 나타났다. 둘째, 최적인출비율은 가입연령과 관계없이 유사한 추세로 나타났다. 셋째, 은퇴자의 상속동기가 감소할수록 그리고 한계연령에 가까워짐에 따라 최적인출비율은 빠르게 증가하였다. 마지막으로 인출펀드의 주식투자 비중이 증가할수록 생애기간 전체의 기대소비액과 사망 시 기대상속액이 모두 증가하는 것으로 나타나났다.
Abstract
As for the design of optimal pension payout plans, unlike the study in literatures minimizing the probability of ruin in retirement accounts, we drive out the time-path optimal withdrawal rates maximizing the individual lifetime utility. Due to multi-period non- linear dynamic optimization problem, we use a genetic algorithm for numerical solutions, which has long been recognized as powerful tools for optimizing complex problems where traditional methods do not apply. The main findings are that (i) the optimal withdrawal rate maintains around 10% at the beginning of the period and increases gradually with time, (ii) time-path optimal withdrawal trends are somewhat similar regardless of the starting age of withdrawal, (iii) optimal withdrawal rates is rapidly increasing as the bequest motives are declining and lastly, expected utility of consumptions and expected utility of bequests each increase on the whole with increase of equity portion in withdrawal funds.
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