Continuous-time Optimization Research Articles

Comments on “Continuous-Time Optimization Model for Source-Sink Matching in Carbon Capture and Storage Systems”

Comments on “Continuous-Time Optimization Model for Source-Sink Matching in Carbon Capture and Storage Systems”

Detection of Arc in the Transmission Power Lines

One- and three-phase automatic reclosing of power lines, after short circuit shutdown, is a very effective way to improve the reliability of power delivery. Re-closing while the fault is not cleared can be dangerous for some electrical appliances. This paper provides a description of two optimization methods concerning the detection of arc in the transmission power lines. The first method is based on least squares approach (LS) and second on total least squares approach (TLS). In order to identify a short-circuit arc, it is proposed to use the degree of distortion of the voltage curve at the beginning of the line, therefore the both methods are based on the estimation of parameters in real-time voltage signals and an analysis of error estimation. An artificial neural network has been proposed to solve the problem in real time. The problems are formulated as optimization tasks and solved using the steepest descent continuous-time optimization algorithm. The network based on the TLS criterion realizes the optimization process under the assumption that the signal model can also be deteriorated (frequency or sampling interval fluctuation and so forth). In comparison to LS estimation, the TLS estimation effect is more reliable when higher sampling frequency and a wider sampling window is applied. The benefit of this research is the innovative possibility of fast detection of arcing faults in real time.

Dynamic product acquisition in closed loop supply chains

We consider a closed-loop supply chain where demand can either be satisfied by manufacturing new products or by buying back used products from customers and upgrading their functionality by remanufacturing. A joint buy-back pricing and manufacturing–remanufacturing decision model at the operations–marketing interface is presented that allows for dynamic parameters, e.g. product life cycles and seasonal aspects. The model allows the identification of beneficial opportunities for buying back and storing used products for immediate and future recovery. We present a new deterministic, dynamic, continuous-time optimisation model, derive necessary and sufficient optimality conditions, and develop a solution algorithm to find the cost-minimising manufacturing and remanufacturing policies as well as buy-back strategies for used products based on Pontryagin's Maximum Principle. It is shown that, in general, an optimal policy will include time intervals where returns are acquired so as to synchronise demand and remanufacturing, where returns are acquired and stored for future remanufacturing, and intervals where demand is satisfied by a mix of manufactured and remanufactured products. Furthermore, we discuss several reactive and proactive acquisition and remanufacturing heuristics and show under which conditions they are optimal. The findings are illustrated by numerical examples.

Continuous-Time Optimization Model for Source–Sink Matching in Carbon Capture and Storage Systems

Carbon capture and storage (CCS) is widely considered to be an essential technology for reducing carbon dioxide (CO2) emissions from sources such as power plants. It involves isolating CO2 from exh...

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION

The objective of this paper is to study the mean–variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in Basak and Chabakauri where the authors assumed a constant risk aversion parameter. This assumption leads to an equilibrium control where the dollar amount invested in the risky asset is independent of current wealth, and we argue that this result is unrealistic from an economic point of view. In order to have a more realistic model we instead study the case when the risk aversion depends dynamically on current wealth. This is a substantially more complicated problem than the one with constant risk aversion but, using the general theory of time‐inconsistent control developed in Björk and Murgoci, we provide a fairly detailed analysis on the general case. In particular, when the risk aversion is inversely proportional to wealth, we provide an analytical solution where the equilibrium dollar amount invested in the risky asset is proportional to current wealth. The equilibrium for this model thus appears more reasonable than the one for the model with constant risk aversion.

Optimality conditions in a vector continuous-time optimization problem

We consider nonlinear vector continuous-time optimization problems with inequality type of constraints. We derive new Fritz John and Karush–Kuhn–Tucker optimality conditions that are valid when all functions are preinvex.

Optimal Portfolios with Stochastic Short Rate: Pitfalls when the Short Rate is Non-Gaussian or the Market Price of Risk is Unbounded

The aim of this paper is to highlight some of the problems occuring when one leaves the usual path of portfolio problems with Gaussian interest rates and bounded market price of risk. We solve several portfolio problems for different specifications of the short rate and the market price of risk. More precisely, we consider a Gaussian model, the Cox-Ingersoll-Ross model, and squared Gaussian as well as lognormal specifications of the short rate. Even for the seemingly innocent Gaussian model, the problem may explode in a certain sense if the market price of risk is unbounded. From an economic point of view, in this case the model does not exhibit a partial equilibrium indicating that, for instants, the time-preferences of the investor are not properly modeled. This problem can be overcome by introducing short rate depending time preferences. Above all, we strongly emphasize that it is not straightforward to generalize the existing results on continuous-time portfolio optimization to the case of a Non-Gaussian stochastic short rate or to a Gaussian term structure with unbounded market price of risk.

KKT Optimality Conditions and Nonsmooth Continuous Time Optimization Problems

We introduce a concept of generalized invexity for the nonsmooth continuous time optimization problems, namely, the concept of Karush-Kuhn-Tucker (KKT) invexity. Then, we prove that this notion is necessary and sufficient for global optimality of a KKT point. We also extend the notion of weak-invexity for nonsmooth continuous time optimization problems. Further, we show that weak-invexity is a necessary and sufficient condition for weak duality.

The minimum wage and labor market outcomes

In The Minimum Wage and Labor Market Outcomes, Christopher Flinn argues that in assessing the effects of the minimum wage (in the United States and elsewhere), a behavioral framework is invaluable for guiding empirical work and the interpretation of results. Flinn develops a job search and wage bargaining model that is capable of generating labor market outcomes consistent with observed wage and unemployment duration distributions, and also can account for observed changes in employment rates and wages after a minimum wage change. Flinn uses previous studies from the minimum wage literature to demonstrate how his model can be used to rationalize and synthesize the diverse results found in widely varying institutional contexts. He also shows how observed wage distributions from before and after a minimum wage change can be used to determine if the change was welfare-improving. More ambitiously, and perhaps controversially, Flinn proposes the construction and formal estimation of the model using commonly available data; model estimates then enable the researcher to determine directly the welfare effects of observed minimum wage changes. This model can be used to conduct counterfactual policy experiments--even to determine optimal minimum wages under a variety of welfare metrics. The development of the model and the econometric theory underlying its estimation are carefully presented so as to enable readers unfamiliar with the econometrics of point process models and dynamic optimization in continuous time to follow the arguments. Although most of the book focuses on the case where only the unemployed search for jobs in a homogeneous labor market environment, later chapters introduce on-the-job search into the model, and explore its implications for minimum wage policy. The book also contains a chapter describing how individual heterogeneity can be introduced into the search, matching, and bargaining framework.

DYNAMIC PORTFOLIO SELECTION UNDER CAPITAL-AT-RISK WITH NO SHORT-SELLING CONSTRAINTS

Portfolio optimization under downside risk is of crucial importance to asset managers. In this article we consider one such particular measure given by the notion of Capital at Risk (CaR), closely related to Value at Risk. We consider portfolio optimization with respect to CaR in the Black-Scholes setting with time dependent parameters and investment strategies, i.e., continuous-time portfolio optimization. We review the results from our previous work in unconstrained portfolio optimization, and then investigate and solve the corresponding problems with the additional constraint of no-short-selling. Analytical formulae are derived for the optimal strategies, and numerical examples are presented.

Continuous-Time Optimal Portfolio Selection Strategy with Redemption Based on Stochastic Control

In this paper a continuous-time portfolio optimization decision with the redemption is made, a typical portfolio selection model is established by use of Bellman principle of optimality and HJB equation, we derive the optimal strategy and efficient frontier with general stochastic control technique. Its research methodologies can be applied in the practical work such as investment funds management and financial risk management to raise the scientificity of decisions. It is of great referential and inspirational value to provide solutions to practical problem in real investment process.

Consumption, Investment and Life Insurance Under Different Tax-Regimes

We study the effects of introducing taxation in classical continuous-time optimization problems with utility from consumption, bequest and retirement savings. Inspired by actual tax-favored retirement savings programs, we formulate and solve the optimization problem for various tax-regimes, and compare tax-effects on consumption/savings contributions, investment and purchase of life insurance under the regimes. The optimization problems have analytical solutions, which allow for easy comparison of tax-effects under the different regimes. To substantiate the results we also present a numerical analysis of the results based on realistic parameter values and regimes. Based on American and Danish tax regimes we estimate the values of existing retirement saving favoring to be 1-2 percent of lifetime income.

BANKING AND BORROWING IN THE EU ETS: A REVIEW OF ECONOMIC MODELLING, CURRENT PROVISIONS AND PROSPECTS FOR FUTURE DESIGN

Abstract This paper deals with the issue of banking and borrowing in the context of the European Union Emissions Trading Scheme (EU ETS) by attempting to provide a policy‐oriented unifying theoretical framework. After describing the main features of the EU ETS, the core part of the paper consists of variations of an intertemporal continuous time optimization model. Additional elements include flexibility measures currently discussed and proposed in other emissions trading systems (USA, Australia), which include the use of safety valves, minimum price auctioning or offsets from domestic or international projects.

Dynamic Pricing and Inventory Policies: A Strategic Analysis of Dual Channel Supply Chain Design

This paper presents a continuous time optimization model for a dynamic pricing and inventory control problem in a dual-channel supply chain system. We consider a manufacturer's redesign of traditional channel structures, based on customer behaviors, by engaging in direct Internet sales. While the manufacturer and its retailer set optimal pricing and inventory policies dynamically, this study considers both vertical integration and competition of two channels. For the former case, a continuous time optimal control problem is modeled, while for the latter a differential quasi-variational inequality (DQVI) formulation is applied to solve as a Cournot-Nash-Bertrand game. We provide implications for optimal strategies and note the effect of a customer acceptance index. [Service Science, ISSN 2164-3962 (print), ISSN 2164-3970 (online), was published by Services Science Global (SSG) from 2009 to 2011 as issues under ISBN 978-1-4276-2090-3.]

Decision Model for Global Manufacturing and Operating Flexibility: Real Options Approach

Abstract This study develops the batch production model of single firm, N sale points, single goods, and adding transport cost of N sale points, which choose one production from N production location (N countries, respectively), and applies the real options approach (ROA) to determine the value of locating production in N countries. A closed-form solution of the optimal transfer threshold value and expected arrival time concerning the firm’s decisions to transfer production location by the ROA and net present value (NPV) method and the continuous-time model optimization problem are derived. Moreover, we get the parameters of how to reciprocally influence optimal transfer threshold values among N countries. Next, given the values of 88-piece parameters in the research model, we can get optimal transfer threshold values from country-0 to country-1, country-2, and country-3, respectively, and more important insights such as that real exchange rate volatility influences expected arrival time for a firm that decides to transfer the production location by the ROA and NPV and the optimal transfer threshold value for a firm that decides to transfer the production location by the ROA. We give an example to explain how to operate this model, and a useful summary of insights is provided for global operation managers.

Existence of solutions in continuous-time optimal growth models

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.

Optimizing Location Among Three Countries Under Exchange Rate Uncertainty: Applying Real Options

This investigation extends the Batch Process Model [Lin et al. (2002). Journal of management and system 9: 173–196] from two productive locations between two countries to establish a decision valuation model for selecting the optimal location of three productive locations among three countries, respectively. A general form with the first order of degree homothetic production functions is also considered by the rule of decision-making in the proposed model. The firm is risk neutral and this study adopts the real options approach for valuing the behavior of the transferable location among three countries. Furthermore, using Dynamic programming and Lagrange Multiplies for a continuous-Time Model Optimization Problem to get a closed form solution of the threshold value, sensitivity analysis, and some characteristic strategies of the operating method for batch process model among three countries are sought, providing for another way of thinking.

Continuous-time optimization problems involving invex functions

In [D.H. Martin, The essence of invexity, J. Optim. Theory Appl. 47 (1985) 65–76] Martin introduced the notions of KKT-invexity and WD-invexity for mathematical programming problems. These notions are relaxations of invexity. In this work we generalize these concepts for continuous-time nonlinear optimization problems. We prove that the notion of KKT-invexity is a necessary and sufficient condition for global optimality of a Karush–Kuhn–Tucker point and that the notion of WD-invexity is a necessary and sufficient condition for weak duality.

Making Investment Choices as Simple as Possible: An Analysis of Target Date Retirement Funds

Many participants in self-directed retirement plans (401k, IRA, etc.) do not know enough about investing to choose rationally among alternatives. Others may know enough, but find it unpleasant or too time-consuming. Target-date (TDFs), also known as life-cycle funds, are being offered as a simple solution to their dilemma. A TDF is a of funds diversified across stocks, bonds, and cash with the feature that the proportion invested in stocks is automatically reduced as time passes. Empirical evidence suggests that a simple TDF strategy would be an improvement over the choices currently made by many uninformed plan participants. This paper explores one way to achieve an even greater improvement. Using a compact continuous-time optimization model, we characterize a person for whom a TDF strategy would be optimal: a TDF holder. We then show that the TDF strategy may be far from optimal for people who — although of the same age — differ from the natural TDF holder in their risk aversion or exposure to human-capital risk. To bring such plan participants much closer to their optimal strategy it is enough to add a second simple investment alternative — a safe fund matched to their time horizon. Participants with the same time horizon could then choose (or be advised to choose) either the TDF or the safe target-date fund depending on their risk aversion and human-capital risk. We find that people who are very risk averse and who have a high exposure to market risk through their labor income would experience a substantial gain in welfare from being offered a safe target-date fund rather than a risky one. Recent empirical research suggests that human-capital betas change over one's working career. They are typically quite high during the early years when human capital represents the largest part of total wealth for most people, and they decline with age. To reflect gradual changes in human capital risk over the life-cycle from predominantly stock-like to mostly bond-like, TDFs should switch from a linear strategy to a hump-shaped strategy with respect to age.

INTERNATIONAL ASYMMETRY IN BUSINESS ACTIVITY AND APPRECIATION OF A STAGNANT COUNTRY'S CURRENCY*

This paper develops a two-country, two-commodity continuous-time dynamic optimization model that accommodates a liquidity trap and persistent unemployment. It investigates a theoretical possibility of international asymmetry in business activity and a stagnant country’s currency appreciation, which has been the common experience of Japan and the USA after Japan’s total capital liberalization. It is found that if the marginal utility of consumption relative to that of liquidity exogenously declines in a country, its current account improves and the home currency appreciates. Consequently, home products lose competitiveness, causing home employment to decrease and foreign employment to increase.