• Journal of applied mathematics & informatics
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• v.39 no.1_2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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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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• v.20 no.2
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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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• v.18 no.4
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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.

• Korean Journal of Social Welfare Studies
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• v.42 no.3
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• pp.291-327
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• 2011

The purpose of this study is to classify the type of retirement process among the mature-aged in Korea. The study used the panel data from Korean Labor Panel (year2~6) for the classification of retirement process through Optimal Matching and Cluster Analysis. Classification is made in 5 categories as 'peripheral-economically active', 'private-transfer dependent', 're-entering limited', 'securely exiting', 'exit-and-reentering'. First, "peripheral-economically active" is a group which frequently experienced job status change and work insecurity. Second, "private-transfer dependent" is a group in which private transfer is likely to be supplements income in the incidence of unemployment. Third, "re-entering limited" is a group in which the proportion of no financial support combined with the absence of any economic activity is the largest. Fourth, the type "Securely exit" is th group whose members switches over to non-economically active status with pension receipt. The last type is "exit-and-reenter" that the member are highly possible to reenter in the labor market and stay in long time regardless of with or without pension plan. To examine the inequality among the types of retirement process, the duration of each status is analyzed. First, in the situation of being non-economically active, the duration of status is maintain public pension receiving and duration stabile in "securely exit" group. For "private-transfer dependent" type, members are mostly dependent on private financial support and that duration of it is longest. Through the analysis of retirement process without under other financial supports, it is "securely-exiting" type for which the duration of full-time employment is longest. It appears that the duration of part-time employment is longest in "peripheral-economically active" type. And for the case of non-waged employment it is "exit-and-reenter" type. Finally, the redistribution policy based on life course perspective is necessary to prevent that the opportunity in the structure before retirement stage and the unfavorable position in labor market make worse disadvantage in retirement process and after that.

• The Korean Journal of Financial Management
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• v.25 no.4
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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.

• Korean Management Science Review
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• v.27 no.1
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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.

• IE interfaces
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• v.24 no.3
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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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.3
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• pp.151-157
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• 2021

This paper deals with financing an early retirement scheme problem(FERSP) with minimum initial cash and filling up maximum financial interest. For this problem, Guéret et al. programming the Mosel, and Edvall merely realize the CPLEX Branch-and-Cut MIP Solver program to get the optimal solution. But there is no clear rule to finding the solution. This paper suggests calculation formula of bond number decision-making that the reverse from long arrival due date to short. Then we optimize and confirm the bonds number in accordance with continuative effect of the arrival due date. The shortage prepare with the principal and interest of one year deposit(saving) reversely calculation formula.