• Korean Management Science Review
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• v.33 no.1
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• pp.77-87
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• 2016

I study optimal consumption and investment choices of an infinitely-lived economic agent with a general time-separable von Neumann-Morgenstern utility under general borrowing constraints against future labor income. An explicit solution is provided by the dynamic programming method. It is shown that the optimal consumption and risky investment decrease as the borrowing constraints become stronger.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.43-47
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• 2013

This paper studies an optimal consumption and portfolio choice problem for unemployed people who have an option to work. Our problem is to find optimal consumption, risky investment, and workforce re-entry strategies for the unemployed. We find a closed form of the critical wealth level to re-enter the workforce. We show that the unemployed with a higher disutility of labor or a larger relative risk aversion are more reluctant to re-enter the workforce.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.43-48
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• 2003

We consider a consumption and investment problem where an investor's investment opportunity gets enlarged when she becomes rich enough, i.e., when her wealth touches a critical level. We derive optimal consumption and investment rules assuming that the investor has a time-separable von Neumann-Morgenstern utility function. An interesting feature of optimal rules is that the investor consumes less and takes more risk in risky assets if the investor expects that she will have a better investment opportunity when her wealth reaches a critical level.

• Korean Management Science Review
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• v.30 no.1
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• pp.167-181
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• 2013

We investigate the dynamic asset allocation problem under inflation risk when the wealth of an investor is constrained with minimum requirements. To capture the investor's risk preference, the CRRA utility function is considered and he maximizes his expected utility at predetermined date of the refund by participation in the financial market. The financial market is supposed to consist of three kinds of financial instruments which are a risk free asset, a risky asset, and an index bond. The role of an index bond is managing inflation risk represented by price process. The optimal wealth and the optimal asset allocation are derived explicitly by using the method to get the European call option pricing formula. From the numerical results, it is confirmed that the investments on index bond is high when the investor's wealth level is low. However, as his wealth increases, the investments on index bond decreases and he invests on risky asset more. Furthermore, the minimum wealth constraint induces lower investment on risky asset but the effect of the constraints is reduced as the wealth level increases.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.2
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• pp.49-66
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• 2014

This paper studies optimal consumption and investment behaviors of an individual when risky asset returns and her income are affected by the business cycle. The investor considers the incomplete information risk of unobservable macroeconomic conditions and updates her belief of expected risky asset returns through Bayesian learning. We find that the optimal investment strategy, certainty equivalent wealth, and portfolio hedging demand significantly depend on the belief about the macroeconomic conditions.

• East Asian Economic Review
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• v.25 no.3
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• pp.310-336
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• 2021

We use iterative numerical procedures combined with analytical methods due to Rapach and Wohar (2009) to solve for the dynamic asset allocation strategy for optimal portfolio demand. We compare different optimal portfolio demands when investors in each country have different access to overseas and domestic investment opportunities. The optimal dynamic asset allocation strategy without foreign investment opportunities leads domestic investors in Korea, Hong Kong, and Singapore to allocate more funds to domestic bonds than to domestic stocks. However, the U.S. investors allocate more wealth to domestic stocks than to domestic bonds. Investors in all countries short bills at a low level of risk aversion. Next, we investigate dynamic asset allocation strategy when domestic investors in Korea have access to foreign markets. The optimal portfolio demand leads investors in Korea to allocate most resources to domestic bonds and foreign stocks. On the other hand, the portfolio weights on foreign bonds and domestic stocks are relatively low. We also analyze dynamic asset allocation strategy for the investors in the U.S., Hong Kong, and Singapore when they have access to the Korean markets as overseas investment opportunities. Compared to the results when the investors only have access to domestic markets, the investors in the U.S. and Singapore increase the portfolio weights on domestic stocks in spite of the overseas investment opportunities in the Korean markets. The investors in the U.S., Hong Kong, and Singapore short domestic bills to invest more than initial funds in risky assets with a varying degree of relative risk aversion coefficients without exception.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1467-1483
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• 2019

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.311-335
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• 2022

This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.

• Journal of the Korea Society for Simulation
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• v.33 no.1
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• pp.27-34
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• 2024

This study aims to propose an optimal asset allocation that minimizes the risk of insufficient realized replacement rates compared to the OECD average replacement rate. To do this, we set the shortfall risk of replacement rates and calculates an asset allocation plan to minimize this risk based on the period of enrollment, the income level and additional contribution. We consider stocks and deposits as investment assets, using Monte Carlo simulation with a GBM model to generate return distributions for stocks. Our result show that, for individuals with a enrollment period of less than 30 years, participants should invest a minimum of 70-80% of their funds in risky assets to minimize the shortfall risk. However, the proportion of funds that need to be invested in risky assets declines significantly when participants contribute an additional premiums. This effect is particularly pronounced among low-income individuals. Therefore, to achieve OECD average replacement rates, the government needs to incentivize participants to invest more in risky assets, while also providing policies to encourage additional contributions, especially for the low-income population.

• The Korean Journal of Financial Management
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• v.2 no.1
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• pp.55-75
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• 1986

This article is to analyse the economic efficiency of capital market, which plays a role of resource allocation in terms of financial claims such as stock and bond. It provides various contributions to the welfare theoretical aspects of modern capital market theory. The key feature that distinguishes the theory described here from traditional welfare theory is the presence of uncertainty. Securities has time dimensions and the state and outcome of the future are really uncertain. This problem resulting from this uncertainty can be solved by complete market, but it has a weak power to explain real stock market. Capital Market is faced with the uncertainity because it is a kind of incomplete market. Individuals and firms in capital market made their consumption-investment decision by their own criteria, i. e. the maximization of expected utility form intertemporal consumption and the maximization of the market value of firm. We noted that allocative decisions that had to be made in the economy could be naturally subdivided into two groups. One set of decisions concerned the allocation of first-period resources among consumption $C_i$, investment in risky firms $I_j$, and riskless investment M. The other decisions concern the distribution among individuals of income available in the second period $Y_i(\theta)$. Corresponing to this grouping, the theoretical analysis of efficiency has also been dichotomized. The optimality of the distribution of output in the second period is distributive efficiency" and the optimality of the allocation of first-period resources is 'the efficiency of investment'. We have found in the distributive efficiency that the conditions for attainability is the same as the conditions for market optimality. The necessary and sufficient conditions for attainability or market optimality is that (1) all utility functions are such that -$\frac{{U_i}^'(Y_i)}{{U_i}^"(Y_i)}={\mu}_i+{\lambda}Y_i$-linear risk tolerance function where the coefficients ${\mu}_i$ and $\lambda$ are independent of $Y_i$, and (2) there are homogeneous expectations, i. e. ${\Large f}_i(\theta)={\Large f}(\theta)$ for every i. On the other hand, the efficiency of investment has disagreement about optimal investment level. The investment level for market rule will not generally lead to Pareto-optimal allocation of investment. This suboptimality is caused by (1)the difference of Diamond's decomposable production function and mean-variance valuation model and (2) the selection of exelusive investment or competitive investment. In conclusion, this article has made an analysis of conditions and processes of Pareto-optimal allocation of resources in capital marker and tried to connect with significant issues in modern finance.