Hyeng Keun Koo

Consumption and portfolio selection with labor income: A discrete-time approach

Abstract. This paper studies the consumption and portfolio selection problem of an agent who is liquidity constrained and has uninsurable income risk in a discrete time setting. It gives properties of optimal policies and presents numerical solutions. The paper, in particular, shows that liquidity constraints and uninsurable income risk reduce consumption and investment in the risky asset substantially from the levels for the case where no market imperfections exist. This paper also shows how the agent evaluates his or her human capital and relates the evaluation to optimal decisions.

A preference change and discretionary stopping in a consumption and porfolio selection problem

We study an optimal consumption-portfolio selection problem in which an economic agent is able to choose a discretionary stopping time in a continuous-time framework. We focus on studying the problem for the case where the agent’s preference changes around the stopping time. We obtain the optimal policy in an explicit form by solving free boundary value problems. If the agent’s coefficient of relative risk aversion becomes higher (lower) after the stopping time, then the optimal policy is to stop as soon as the wealth level touches down (up) to the critical wealth level.

A SURVEY ON AMERICAN OPTIONS: OLD APPROACHES AND NEW TRENDS

This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European op- tion can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up un- til now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These ap- proaches typically provide numerical or approximate analytic methods to �nd the price and the boundary. Topics included in this survey are early approaches(treesnite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, an- alytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochas- tic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

Optimal consumption and portfolio selection with quadratic utility and a subsistence consumption constraint

ABSTRACT In this article, we analyze the optimal consumption and investment policy of an agent who has a quadratic felicity function and faces a subsistence consumption constraint. The agents optimal investment in the risky asset increases linearly for low wealth levels. Risk taking continues to increase at a decreasing rate for wealth levels higher than subsistence wealth until it hits a maximum at a certain wealth level, and declines for wealth levels above this threshold. Further, the agent has a bliss level of consumption, since if an agent consumes more than this level she will suffer utility loss. Eventually her risk taking becomes zero at a wealth level which supports her bliss consumption.

Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function

We propose and solve a general entrepreneurial/managerial decision-making problem. Instead of employing concave objective functions, we use a broad class of nonconcave objective functions. We approach the problem by a martingale method. We show that the optimization problem with a nonconcave objective function has the same solution as the optimization problem when the objective function is replaced by its concave hull, and thus the problems are equivalent to each other. The value function is shown to be strictly concave and to satisfy the Hamilton-Jacobi-Bellman equation of dynamic programming. We also show that the final wealth cannot take values in the region where the objective function is not concave: the entrepreneur would like to avoid her or his wealth ending up in the nonconcave region. Because of this, the entrepreneur’s risk taking explodes as time nears maturity if her his wealth is equal to the right end point of the nonconcave region.

A simple asset pricing model with heterogeneous agents, uninsurable labor income and limited stock market participation

In this paper we study a simple two-period asset pricing model to understand the implications of uninsurable labor income risk and/or borrowing constraints, limited stock market participation, heterogeneous labor income volatilities, and heterogeneous preferences. We appraise the performance of each of these in matching moments of asset returns to the data and show that limited stock market participation generates a significantly large equity premium. We also show that the distribution of wealth between stock market participants and non-participants plays an important role in asset pricing, and that the effect of borrowing constraints on asset returns are similar to that of limited participation. Finally, we discuss the practical implications of our investigation, providing an appraisal of ongoing changes in asset returns.

Option pricing and Greeks via a moving least square meshfree method

We apply a meshfree method using the fast moving least squares approximation to option pricing, particularly for the purpose of obtaining high-order Greeks. The method is shown to be accurate and efficient in obtaining prices and Greeks of European, Asian and Barrier options. We also include a complicated Equity Linked Security (ELS) from the Korean OTC market, as a real-world example.

Endogenous Credit Constraints and Household Portfolio Choices

We study a continuous-time model of consumption and portfolio selection with limited commitment in a stochastic environment. The credit constraints of a household are determined endogenously in the credit market where creditors know that the household is not committed to payment of debt. By using a duality approach, we transform the problem into a dual minimization problem and subsequently into optimal stopping problems. We derive the time-varying endogenous credit limit and optimal consumption and investment strategies in closed form. We show that the credit limit is cyclical: it is lower (higher) when the Sharpe ratio of the risky asset is high (low). We find that a change in the credit limit and the counter-cyclical Sharpe ratio generate a heterogeneous investment pattern: the rich tend to increase the proportion of risky investment in downturns whereas the poor decrease it, a finding supported by the Survey of Consumer Finance data.

Optimal Consumption and Portfolio Selection with Early Retirement Option

In this paper we propose an approach to investigate a model of consumption and investment with a mandatory retirement date and early retirement option; we analyze properties of the optimal strategy and thereby contribute to understanding the interaction between retirement, consumption, and portfolio decisions in the presence of both the important features of retirement. In particular, we provide a characterization of the threshold of wealth as a function of time, and we show that it is strictly decreasing near the mandatory retirement date. The threshold is similar to the early exercise boundary of an American option in the sense that if the agent’s wealth is above or equal to the threshold level, then the agent immediately retires. We also provide comparative static analysis.

Optimal Hedging of a Contingent Claim with Ambiguity Aversion

We propose a model of hedging and investment with ambiguity aversion in an incomplete financial market. We show that the agents worst-case belief depends upon the payoff of the derivative to be hedged. Thus, we identify situations where one can distinguish ambiguity averse agents from probabilistically sophisticated agents. Further, we generate the hypothesis: an ambiguity averse agent chooses higher volatility when hedging a derivative position whose payoff function is convex than when hedging a position whose payoff function is concave. Our model can be extended to accommodate non-iid uncertainty and jumps in the continuous time limit of the model.