Optimal stopping time with stochastic volatility

This paper demonstrates how to convert a path-dependent optimal stopping time problem into a path-independent problem using a transformation analysis method. We test this method to deal with several problems, especially those in stochastic volatility environments. We introduce stochastic state variables into volatility dynamics and analyse the influence of state-variable volatile characters on investment stopping boundaries. For arbitrary coefficient circumstances, we set up a Riccati equation that satisfies the transformation. For circumstances involving Heston stochastic-volatility, we propose an analytical solution. This paper extends research on the optimal investment stopping issue to a stochastic investment opportunity environment. Our proposed method can enhance the ability of optimal investment stopping theory to describe the real capital market.     

Mineral resources for renewable energy: Optimal timing of energy production

The production of energy from renewable sources is much more intensive in minerals than that from fossil resources. The scarcity of certain minerals limits the potential for substituting renewable energy for scarce fossil resources. However, minerals can be recycled, while fossil resources cannot. We develop an intertemporal model to study the dynamics of the optimal energy mix in the presence of mineral intensive renewable energy and fossil energy. We analyze energy production when both mineral and fossil resources are scarce, but minerals are recyclable. We show that the greater the recycling rate of minerals, the more the energy mix should rely on renewable energy, and the sooner should investment in renewable capacity take place. We confirm these results even in the presence of other better known factors that affect the optimal schedule of resource use: expected productivity growth in the renewable sector, imperfect substitution between the two sources of energy, convex extraction costs for mineral resources and pollution from the use of fossil resources.     

Measuring consumption efficiency with utility theory and stochastic frontier analysis

The concept of production efficiency has been studied since the 1960s, but consumption activity as well may be inefficient for various reasons, such as product complexity, lack of information, the bounded rationality of the consumer and imperfect markets, to name a few. This study proposes a conceptual framework for measuring the consumption efficiency of differentiated products, based on traditional utility theory. It employs stochastic frontier analysis (SFA) in an empirical analysis. It makes use of hedonic price theory to link traditional utility theory and the SFA framework. When the developed model is applied to the Korean personal computer market, empirical results indicate the levels and distribution of consumption efficiency in that market. The findings afford us a better understanding of the characteristics of the innovation process in that market.     

Optimal investment and consumption with return predictability and execution costs

We provide a closed-form solution to an optimal investment and consumption problem for a constant absolute risk aversion (CARA) agent, who faces execution costs when trading correlated risky assets with return predictability. The optimal investment strategy indicates that the agent should trade gradually toward a dynamic aim portfolio, which is an adjusted Merton portfolio with modifications to account for the persistence of the return-predicting signals and the execution costs. The optimal consumption strategy is quadratic in the return-predicting signals and linear in the agent's wealth. Our numerical studies show that the execution costs diminish the importance of asset return predictability on the agent's optimal investment strategy, thereby confirming the conjecture raised by Liu (2004). In addition, the presence of the intermediate consumption leads to a more aggressive aim portfolio than the case without consumption.     

Strategic intergenerational bequests with stochastic convex production

Summary This note reconsiders the well-known model of strategic bequest/ altruistic growth, but with stochastic production satisfying a strong convexity condition: The probability that the next stock exceeds any given level is concave in investment. Existence of a Markov-stationary equilibrium consumption schedule, which is continuous and with all slopes in [0,1], is established. Under smooth data and interiority assumptions, this schedule is differentiable, and marginal consumption is in (0,1). This property allows for a rigorous and straightforward treatment of the equilibrium characterization problem.The author is grateful to Wolfgang Leininger for helpful discussions on the subject of this paper. This research work was carried out while the author was visiting C.O.R.E., Belgium and the University of Dortmund, Germany. The author wishes to thank both institutions for providing a great work environment as well as financial support from the projects Markets as Games and Marktstruktut und Gesamtwirtschaftliche Entwicklung, respectively.     

Optimal procurement strategies by reverse auctions with stochastic demand

This paper studies a dynamic procurement problem by reverse auction for a retailer with stochastic demand. In each period, the retailer based on his inventory needs to determine a payment function (a procurement contract) according to which a number of potential suppliers compete in the reverse auction. We show the existence of the retailer's optimal payment function and find that the suppliers' Bayesian–Nash equilibrium bidding strategy is similar to the base-stock policy in the traditional multi-period inventory control problems when the retailer incurs no fixed setup cost, while similar to the (s, S) policy when the retailer incurs a fixed setup cost. This strategy is for the suppliers, instead of for the retailer, depends on the supplier's marginal cost and so is stochastic for the retailer. Thus, this paper extends well beyond traditional procurement environments studied so far in the inventory control literature.     

Tractable graphical device for analyzing stationary stochastic OLG economies

This article develops a tractable graphical device for analyzing the stationary, stochastic overlapping generations economy. In this paper, the graphical device is applied to the theoretical study on stochastic bubbles per Weil (1987) and gives new insights into the issue.     

Optimal steady-state in stationary consumption-loan type models

We consider a stationary overlapping generations economy, and prove that an optimal steady state exists. We show that if a government intervention is needed in order to implement the optimal steady state as a competitive equilibrium, it is necessary only in a finite number of periods. If the interest rate associated with the optimal steady state equals the population rate of growth, some outside money may be required in order to make the competitive equilibrium follow the optimal steady state. We show that our existence result enables us to construct Pareto optimal competitive equilibria in some important cases.     

Optimal retirement age,leisure and consumption

In this paper, we study the determination of optimal retirement age, optimal leisure time, and optimal consumption, and we also analyze their relationships using an optimal control theory. We establish a life cycle model and analyze the factors of consumption, leisure, saving, mortality and retirement behaviors simultaneously with an orthogonal-array experimental design. Our results show that the initial salary level and the growth rate of salary are the most important determining factors of the optimal retirement age. The initial consumption level and the interest rate are also important factors affecting optimal retirement age. The mortality improvement has a minor effect on the optimal retirement age. The effects of the Social Security on the optimal retirement age depend on the Social Security tax and the level of Social Security benefit.     

Constant per capita consumption paths with exhaustible resources and decaying produced capital

We introduce decay in produced capital and exogenous technical progress to the recent “Solow Model” of Asheim et al. with population growth and observe the possible collapse of the economy given too high a rate of decay. “Enough” technical progress can restore sustainable per capita consumption.     

Constant per capita consumption paths with exhaustible resources and decaying produced capital

We introduce decay in produced capital and exogenous technical progress to the recent “Solow Model” of Asheim et al. with population growth and observe the possible collapse of the economy given too high a rate of decay. “Enough” technical progress can restore sustainable per capita consumption.     

Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon

This paper considers the multi-period optimal strategies for an investment-only problem and an investment–consumption problem. The financial market is regime-switching and consists of one risk-free asset and multiple risky assets. The state process of the financial market is modeled by a finite-state Markov chain. Asset returns and utility functions are affected by the states of the financial market. The investment time-horizon is uncertain and exogenous. By adopting the dynamic programming approach, explicit expressions for optimal value functions and optimal investment and consumption strategies are derived. Moreover, some discussions and numerical examples are provided to illustrate our results, which extend some results in the existing literature to more general situations and show some interesting phenomena.     

Optimal pricing and investment for resources with alternative uses and capacity limits

Airport runways, radio spectrum, and hospital beds are resources with capacity limits used to provide multiple services with specific capacity requirements in separate markets, which contribute to recover capacity investment costs. A welfare-maximizing and (possibly) budget-constrained firm, whose operating costs significantly increase as total capacity use presses against capacity, chooses prices and capacity. When the equilibrium capacity is reached, second-best Ramsey prices must be adjusted, and mark-ups on marginal costs may be higher for services with higher demand elasticities, if they intensively use capacity. Moreover, for a given output vector, the firm invests more than in first best. Instead, the equilibrium capacity may be first best when there is excess capacity to reduce operating costs and thus improve welfare. Our model can be used as a benchmark to evaluate the efficiency of market mechanisms for resource allocation and pricing, or when market mechanisms are not adopted.

     

Optimal investment strategies in an international economy with stochastic interest rates

We investigate how investors should optimally choose to invest in a dynamically complete international market. We find closed-form solutions for the optimal investment strategy and for the wealth loss an investor suffers from not investing internationally. Theoretically, we show that the gain from international investment is due to the speculative investment only, and why it is important for an investor from a large economy to invest in a small economy. In a numerical example we compare the wealth losses investors from Denmark and the U.S. suffer due to home bias.     

Optimal contracting with dynastic altruism: Family size and per capita consumption

We use a Barro–Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade-off between family size and future consumption and leisure, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.     

Optimal growth when consumption takes time

This article analyzes a one‐sector growth model where the consumption takes time. When the consumption takes time, the consumption set is compact and we meet satiety. However, we prove that dynamic constraints are binding. This result is crucial to prove that, under well‐known assumptions in macroeconomic dynamic programming, the optimal path is monotonic and always converges to a unique nontrivial steady state as in the case where consumption is timeless.     

Optimal disaster-preventive expenditure in a dynamic and stochastic model

The purpose of this study is to present an analytical framework for publicly optimal disaster-preventive expenditure. We examine the optimal policy combination of tax rate, disaster-preventive expenditure, and productive government expenditure in a neoclassical growth model, in which natural disasters occur stochastically and partially destroy existing capital. Based on this model, we can decompose the welfare effect of raising preventive expenditure into three effects: the damage reduction, crowding out, and precautionary effects. By identifying these marginal benefits and costs, we obtain the policy conditions that maximize household welfare. Furthermore, we show that optimal prevention is increasing in disaster probability, and by using a numerical example, we show that there is an inverse U-shaped relationship between the expected growth rate and disaster probability.     

Indefinitely sustained consumption despite exhaustible natural resources

Summary This paper analyzes the feasibility of sustaining uniformly positive consumption forever — even when flows of exhaustible resources are an indispensable input. The main result is a characterization of an economy's capability for sustaining such consumption — under quite general maintained assumptions on technology — in terms of a single, simple capital-resource substitution condition.This is a revised version of CARESS Working Paper #79-27. An even earlier preliminary paper by Mitra [1] contained the seminal idea developed more thoroughly here. Both of our research efforts were supported by the NSF, while much of Cass's participation took place during his tenure as a Sherman Fairchild Distinguished Scholar at Caltech. We thank both institutions for their support and encouragement.