Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk

Does Risk Seeking Drive Asset Prices? A stochastic dominance analysis of aggregate investor preferences

We investigate whether risk seeking or non-concave utility functions can help to explainthe cross-sectional pattern of stock returns. For this purpose, we analyze the stochasticdominance efficiency classification of the value-weighted market portfolio relative tobenchmark portfolios based on market capitalization, book-to-market equity ratio andmomentum. We use various existing and novel stochastic dominance criteria that accountfor the possibility that investors exhibit local risk seeking behavior. Our results suggestthat Markowitz type utility functions, with risk aversion for losses and risk seeking forgains, can capture the cross-sectional pattern of stock returns. The low average yield onbig caps, growth stocks and past losers may reflect investors' twin desire for downsideprotection in bear markets and upside potential in bull markets.asset pricing;stochastic dominance;prospect theory;risk seeking;specification error

An Optimal Execution Problem with S-shaped Market Impact Functions

In this study, we extend the optimal execution problem with convex market impact function studied in Kato (2014) to the case where the market impact function is S-shaped, that is, concave on $[0, \bar {x}_0]$ and convex on $[\bar {x}_0, \infty )$ for some $\bar {x}_0 \geq 0$. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the optimal execution speed under the S-shaped market impact is equal to zero or larger than $\bar {x}_0$. Moreover, we provide some examples of the Black-Scholes model. We show that the optimal strategy for a risk-neutral trader with small shares is the time-weighted average price strategy whenever the market impact function is S-shaped.Comment: 22 pages, 2 figures, forthcoming in "Communications on Stochastic Analysis

Pollution control: targets and dynamics.

In this paper I study the e¤ects of environmental regulation which establishes upper and lower binding targets to pollution emissions. Essentially, I deal with the properties of a stochastic model of pollution control in continuous-time under emission targets and uncertainty, emphasizing dynamic nonlinearities. Inside the targets pollution behaves as if it were freely floating until it hits one of the two limits. The model provides three main results. First, I show that binding targets can affect the pollution floating even when the boundaries are currently slack. Solutions of the model show that pollution becomes an S-shaped locus of the fundamentals. Second, I show that binding targets will lead to more stable pollution rate determination within the boundaries, than free floating. Finally, stabilization of pollution is related to the growth rate and volatility of fundamentals, to the sensitivity to expected changes of pollution rate and to the credibility of the authorities in defending the pollution targets.Pollution targets, Optimal stochastic control, Uncertainty, Environmental policy.

Endogenous Technological Change under Uncertainty

How does risk or uncertainty in the productivity of research affect the growth rate of the economy? To answer this question, a model of endogenous technological change is used where sustained growth stems from intentional investments in R&D from profit-maximizing firms. The uncertainty arises from the productivity of these investments in R&D. The main result of this analysis is that the relationship between long-run growth and uncertainty (on the productivity of knowledge creation) depends on two main factors - the returns to scale in knowledge creation (increasing or non-increasing) and the value of the elasticity of intertemporal substitution (higher or lower than some critical value). Based on empirical studies on the returns to scale in knowledge creation (”non-increasing”) and the value of the elasticity of intertemporal substitution (”higher than the critical value”), we expect a negative relationship between long-run growth and uncertainty regarding the productivity of knowledge creation.Long-run growth, Technological change, Uncertainty

Output dynamics in an endogenous growth model

The aim of this paper is to analyze whether endogenous growth RBC models are consistent with two stylized facts about U.S. output dynamics. First, GNP growth is positively correlated in the short run and it has a weak negative autocorrelation over longer horizons. Second, GNP appears to have an important trend-reverting component that has a hump-shaped MA representation. In particular, this article considers a stochastic version of Lucas' (1988) model in the absence of externalities in discrete time with two modifications: agents derive utility not only from consumption but also from leisure and labor adjustment costs are included. Results reveal that combining the endogenous character of the engine of growth with labor adjustment costs may help solve the Cogley-Nason (1995) puzzle since it provides a stronger propagation mechanism which, in turn, improves the model's ability to generate realistic output dynamics.real business cycle models, endogenous growth, propagation mechanism

The new keynesian approach to dynamic general equilibrium modeling: models, methods, and macroeconomic policy evaluation

This chapter aims to provide a hands-on approach to New Keynesian models and their uses for macroeconomic policy analysis. It starts by reviewing the origins of the New Keynesian approach, the key model ingredients and representative models. Building blocks of current-generation dynamic stochastic general equilibrium (DSGE) models are discussed in detail. These models address the famous Lucas critique by deriving behavioral equations systematically from the optimizing and forward-looking decision-making of households and firms subject to well-defined constraints. State-of-the-art methods for solving and estimating such models are reviewed and presented in examples. The chapter goes beyond the mere presentation of the most popular benchmark model by providing a framework for model comparison along with a database that includes a wide variety of macroeconomic models. Thus, it offers a convenient approach for comparing new models to available benchmarks and for investigating whether particular policy recommendations are robust to model uncertainty. Such robustness analysis is illustrated by evaluating the performance of simple monetary policy rules across a range of recently-estimated models including some with financial market imperfections and by reviewing recent comparative findings regarding the magnitude of government spending multipliers. The chapter concludes with a discussion of important objectives for on-going and future research using the New Keynesian framework

"Human Capital as an Asset Mix and Optimal Life-Cycle Portfolio: An Analytical Solution"

This study examines life-cycle optimal consumption and asset allocation in the presence of human capital. Labor income seems like a "money market mutual fund" whose balance in one or two years is predictable but a wide dispersion results after many years, reflecting fluctuations in economic conditions. We use the Martingale method to derive an analytical solution, finding that Merton's well-known " constant-mix strategy" is still true after incorporating human capital from the perspective of "total wealth" management. Moreover, the proportion in risky assets implicit in the agent's human capital is the main factor determining the optimal investment strategy. The numerical examples suggest that young investors should short stocks because their human capital has large market exposure. As they age, however, their human capital becomes "bond-like", and thus they have to hold stocks to achieve optimal overall risk exposure.

Human Capital as an Asset Mix and Optimal Life-Cycle Portfolio: An Analytical Solution

This study examines life-cycle optimal consumption and asset allocation in the presence of human capital. Labor income seems like a "money market mutual fund" whose balance in one or two years is predictable but a wide dispersion results after many years, reflecting fluctuations in economic conditions. We use the Martingale method to derive an analytical solution, finding that Mertons well- known "constant-mix strategy" is still true after incorporating human capital from the perspective of "total wealth" management. Moreover, the proportion in risky assets implicit in the agent's human capital is the main factor determining the optimal investment strategy. The numerical examples suggest that young investors should short stocks because their human capital has large market exposure. As they age, however, their human capital becomes "bond-like", and thus they have to hold stocks to achieve optimal overall risk exposure.