Seyoung Park

Optimal retirement strategy with a negative wealth constraint

Abstract This paper investigates an optimal consumption, portfolio, and retirement time choice problem of an individual with a negative wealth constraint. We obtain analytical results of the optimal consumption, investment, and retirement behaviors and discuss the effect of the negative wealth constraint on the optimal behaviors. We find that, as an individual can borrow more with better credit, she is more likely to retire at a higher wealth level, to consume more, and to invest more in risky assets.

When Do the Unemployed Jump in the Workforce

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.

Stock Returns and Market Making with Inventory

We study optimal trading strategy of a market maker with stock inventory. Following Avellaneda and Stoikov (2008), we assume the stock price follows a normal distribution. However, we take a constant expected rate of the stock return and assume that the stock volatility is an inverse function of the stock price level. We show that the optimal bid-ask spread of the market maker is wider for a higher expected rate of stock returns.

Unemployment Risks and Optimal Retirement in an Incomplete Market

We develop a new approach for solving the optimal retirement problem for an individual with an unhedgeable income risk. The income risk stems from a forced unemployment event, which occurs as an exponentially distributed random shock. The optimal retirement problem is to determine an individual’s optimal consumption and investment behaviors and optimal retirement time simultaneously. We introduce a new convex-duality approach for reformulating the original retirement problem and provide an iterative numerical method to solve it. Reasonably calibrated parameters say that our model can give an explanation for lower consumption and risky investment behaviors of individuals, and for relatively higher stock holdings of the poor. We also analyze the sensitivity of an individual’s optimal behavior in changing her wealth level, investment opportunity, and the magnitude of preference for postretirement leisure. Finally, we find that our model explains a countercyclical pattern of the number of unemployed job leavers.

Life-Cycle Consumption, Investment, and Voluntary Retirement with Cointegration between the Stock and Labor Markets

We present an optimal portfolio choice for retiring early when a borrowing and short sale constrained investor is facing cointegration between the stock and labor markets. With reasonable parameter values, there exists a target wealth-to-income ratio under which the investor does not participate in the stock market at all, whereas above which the investor increases the proportion of financial wealth invested in the stock market as she accumulates wealth. Contrary to common intuition, flexibility in determining the retirement timing allows the investor to invest less in the stock market than without retirement flexibility. Finally, the investors willingness to retire earlier becomes stronger as risk aversion increases or as wages decline in the long term.

Marginal Propensity to Consume with a Negative Wealth Constraint

There exists one potential source which has not obtained full treatment in the recent consumption literature: a negative wealth constraint (NWC). An economic agent who faces the NWC can borrow up to a certain proportion of the present value of labor income. We present an analytically tractable consumption-savings and investment model with the NWC. The model can prove one important result: consumption is strictly concave with wealth (Carroll and Kimball, 1996) even when labor income is perfectly riskless. More interestingly, the higher marginal propensity to consume out of financial wealth obtains with the tighter NWC.

Optimal Investment with Time-Varying Transition Probabilities for Regime Switching

In this paper we generalize the following result of McDonald and Siegel (1986) on optimal investment: it is optimal for an investor to invest when project cash flows exceed a certain threshold. We have other results that refine or extend the result of McDonald and Siegel (1986) by integrating timing flexibility and changes in cash flows with time-varying transition probabilities for regime switching. We emphasize that optimal thresholds are either overvalued or undervalued in the absence of time-varying transition probabilities. Accordingly, the stochastic nature of transition probabilities plays important roles in searching for optimal timing of investment.

Consumption, Retirement, and Asset Allocation with Unemployment Risks and Borrowing Constraints

We study optimal consumption, investment, and retirement strategies of an individual subject to a nonnegative wealth constraint and exposed to unhedgeable forced unemployment risks. We find strong evidence that a small chance of forced unemployment can have a significant effect on the individual’s optimal consumption, investment, and retirement behaviors. Comparing a complete market with a private unemployment insurance we show that the market innovation by introduction of private unemployment insurance might increase individuals’ welfare, especially welfare of poor people and people with a low post-retirement leisure preference or who are placed in bad economic conditions.In this paper, we develop a new dynamic programming approach for solving an optimal retirement model in a two-dimensional incomplete market, which is induced by forced unemployment risk and borrowing constraints. We show that the two dimensions jointly affect an individuals optimal consumption, investment, and retirement strategies. Specifically, we find that there exists a certain endogenously determined wealth threshold over which it is optimal for an individual to enter retirement. Comparing to standard literature, the wealth threshold is lower in the presence of the two-dimensional market incompleteness, implying an earlier retirement than would be suggested by a complete market model. As a result, neglecting the two-dimensional market incompleteness can be costly to an individual who aims to attain her goal of optimal retirement.