• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.215-222
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• 2021

We explore an optimal consumption/portfolio and retirement problem with a CARA utility function of consumption. The relevant Bellman equation for the value function is transformed into a linear equation and the optimal strategies are obtained explicitly.

• 충청수학회지
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• 제33권2호
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• pp.293-300
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• 2020

In this paper we study an optimal consumption, investment and retirement time choice problem of an investor who receives labor income before her voluntary retirement. And we assume that there is a negative wealth constraint which is a general version of borrowing constraint. Using convex-duality method, we provide the closed-form solutions of the optimization problem.

• 대한수학회보
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• 제60권4호
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• pp.1101-1129
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• 2023

In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.

• Management Science and Financial Engineering
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• 제20권2호
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• pp.13-25
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• 2014

We investigate an optimal retirement time and consumption/investment policy of a wage earner who expects to find a better investment opportunity after retirement by being freed from other work and participating fully in the financial market. We obtain a closed form solution to the optimization problem by using a dynamic programming method under general time-separable von Neumann-Morgenstern utility. It is optimal for the wage earner to retire from work if and only if his wealth exceeds a certain critical level which is obtained from a free boundary value problem. The wage earner consumes less and takes more risk than he would without anticipation of a better investment opportunity.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권4호
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• pp.283-294
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• 2014

In this paper we study consumption-labor supply decision of an agent who prepares for retirement at a known time in the future. The agent is assumed to have a preference which is represented by the von Neumann-Morgenstern utility function in which the felicity function has constant relative risk aversion over the composite of consumption and leisure. The composite is obtained by the Cobb-Douglas function. A general problem has been studied by Bodie et al. (2004). We contribute to the literature by deriving the Slutsky equations and conducting comparative statics. In particular, we show that wealth effect can exhibit an interesting property depending upon the time until retirement, as the interest rate increases.

• 사회복지연구
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• 제42권3호
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• pp.291-327
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• 2011

본 연구의 목적은 우리나라 중고령자의 은퇴과정을 유형화 하고 다양성과 경제적 불평등에 초점을 두어 각 유형의 특성을 살펴보는 데 있다. 유형화 분석을 위해 한국노동패널 제2~6차년도 자료를 활용하여 탐색적 분석방법인 최적일치법(optimal matching)과 군집분석(cluster analysis)을 적용하였다. 은퇴과정의 유형화 분석결과, 주변적경제활동형, 사적이전의존형, 재진입제약형, 안정적퇴장형, 퇴장후재진입형 5개의 유형을 도출하였다. 각 유형별로 다양한 유형적 특성을 보였는데, 우선 주변적경제활동형은 주변적 근로자에게서 발견되는 전형적인 고용 불안정 특성을 보였다. 둘째, 사적이전의존형은 은퇴과정에서 고용활동 중단 시 사적이전에 의한 소득보전 가능성이 높은 유형이다. 셋째, 재진입제약형은 경제적 지원없이 '비경활-비수급' 상태의 분포가 가장 높은 유형이다. 넷째, 안정적퇴장형은 비경활-연금수급 상태로 이행한 비중이 높은 유형이다. 끝으로, 퇴장후재진입형은 은퇴과정에서 재취업을 하여 늦은 연령기까지 고용상태를 유지할 가능성이 높은 특징을 보였다. 또한 상태별 지속기간 분석을 통해 유형 간 경제적 불평등 상태를 비교해 본 결과, 공적연금 수급 가능성과 수급의 지속성이 가장 안정적으로 이루어지는 유형은 안정적퇴장형이었다. 사적이전의존형은 사적이전의 경제적 지원 가능성이 가장 높고 지속기간도 가장 긴 것으로 나타났다. 그리고 은퇴과정에서 경제적 지원이 없는 상태에서 고용상태에 따른 상태 별 지속기간을 살펴 본 결과, 정규직 지속기간이 가장 긴 유형은 안정적퇴장형이었다. 주변적경제활동형은 은퇴과정에서 비정규직 고용상태의 지속기간이 가장 길게 나타났다. 비임금 근로는 퇴장후재진입형에서 지속기간이 가장 높게 나타났다. 본 연구를 통해 얻을 수 있는 정책적 함의는 생애과정의 초기에 형성된 기회구조와 노동시장에서 불리한 지위로 인해서 은퇴 이후에 불이익이 더 증가되지 않도록 완화하는 생애과정 관점의 재분배정책이 강화되어야 한다는 점이다.

• 재무관리연구
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• 제25권4호
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• pp.145-182
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• 2008

As the life expectancy increases resulting in the aged society, the post-retirement life became one of the most important concerns of people. The long-term investment vehicles such as retirement savings and pension plans have been introduced to meet such demand of society. This paper examines the impact of asset allocation strategies on the long-term investment performance. Because of the unusually long investment horizon and the compounding effect, a suboptimal asset mix in a retirement plan can be a very costly and irreversible mistake. Instead of relying on anecdotal evidence to evaluate the merits of different allocation strategies, this paper performs various tests including stochastic dominance tests using both actual data and Monte Carlo simulated data that best fit the historical experience. The results indicate 1) the long-term investments perform better than the short-term investments, 2) the optimal asset allocation strategy for the long-term investments should be highly equity dominated.

• 경영과학
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• 제27권1호
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• pp.45-60
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• 2010

This study evaluates life annuity plans based on two different types of measures : financial benefit and utility on consumption. The financial benefit is measured by Money's Worth (MW) ratio and return on annuity. For the measure of utility, an optimization problem is formulated with the objective of maximizing utility on consumption. To solve the optimization model, we use Dynamic Programming (DP) technique. The both types of measures are applied to cases of Korean pre-retirees at age 40 with different accumulation years of annuity (i.e. level of annuity asset at the age of retirement) and different timings of annuitization. Our results generally indicate that the utility based optimization model is superior to the financial measures in terms of providing a better evaluation of an annuity plan due to its capability to consider an individual's financial situation during his/her retirement period. Also, they suggest that the level of annuity asset is an important factor when an individual determines the optimal annuitization timing.

• 산업공학
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• 제24권3호
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• pp.173-186
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• 2011

In this paper, we evaluate life annuity plans for Korean pre-retired single and married couple participating Korea National Pension (KNP) and find optimal life annuity strategy by using utility-based measurements called AEW (Annuity Equivalent Wealth). Specifically, we extend a previous study to obtain a detailed optimal combination of annuitizing age and wealth in terms of percentage of net wealth at the time of retirement. A nonlinear optimization model is formulated with the objective of maximizing utility on consumption and bequest, and the dynamic programming (DP) technique is used to solve this problem. We find that there exist consistent patterns in optimal combinations of annuitizing age and wealth. Also, for all cases the optimal combination is significantly better than several other combinations. The results indicate that using the optimal approach can be beneficial to practitioners in insurance industry and prospective purchasers of life annuity. We conclude the paper with some discussions and suggestions.

• 한국인터넷방송통신학회논문지
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• 제21권3호
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• pp.151-157
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• 2021

본 논문은 조기퇴직자들의 퇴직금을 충당하는데 있어 최소의 초기 투자금만으로 최대의 재태크로 인한 수익금으로 충당하는 방법을 다룬다. 이 문제에 대해 Guéret et al.은 Mosel 프로그램을, Edvall은 해를 찾아가는 명확한 규칙없이 단지 CPLEX Branch-and-Cut MIP Solver 프로그램을 구현하여 해를 얻었다. 본 논문에서는 이 문제에 대해 만기도래기간이 긴 채권부터 역으로 채권 수를 결정하는 계산식을 제시하고, 채권 만기도래의 연속적 효과를 고려하여 채권 수 최적화를 수행하여 채권 수를 확정하였으며, 부족액은 역으로 1년만기 적금의 원금과 이자로 충당하는 계산식을 제시하였다.