Hedging entry and exit decisions: optimizing location under exchange rate uncertainty

^** Email: alexru00{at}ms41.hinet.net^*** Email: ctlin{at}mail.yust.edu.tw The Cobb–Douglas production function with Abel's (1983,Am. Econ. Rev., 173, 228–233) model is extended herein,and real options analysis (ROA) for entry–exit decision-makingestablished utilizing Dixit's (1989b) decision model under exchangerate uncertainty. This work considers the effects of real exchangerates on strategies that determine the locations of productionby firms that are entering markets in two countries. The ROAis also adopted to evaluate the switching location between twocountries. A continuous-time model optimization problem is solvedin closed-form. This provides a useful beginning to an importantanalysis of the effects on industry of exchange rate fluctuationswhen the optimal entry (exit) trigger for transferring locationsis important for a basic global logistics model. Furthermore,a myopic solution of the optimal entry (exit) trigger, sensitivityanalysis and some characteristics of the optimal productionstrategy are sought. This paper contributes to the problem ofchoice of foreign production strategy.     

Portfolio optimization with uncertain exit time in infinite-time horizon

In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.     

Game options with gradual exercise and cancellation under proportional transaction costs

ABSTRACT

Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomized) stopping time, rather than instantly at an ordinary stopping time. Allowing gradual exercise and cancellation leads to increased flexibility in hedging, and hence tighter bounds on the option price as compared to the case of instantaneous exercise and cancellation. Algorithmic constructions for the bid and ask prices, and the associated superhedging strategies and optimal mixed stopping times for both exercise and cancellation are developed and illustrated. Probabilistic dual representations for bid and ask prices are also established.     

A compromise solution for the multiobjective stochastic linear programming under partial uncertainty

This paper solves the multiobjective stochastic linear program with partially known probability. We address the case where the probability distribution is defined by crisp inequalities. We propose a chance constrained approach and a compromise programming approach to transform the multiobjective stochastic linear program with linear partial information on probability distribution into its equivalent uniobjective problem. The resulting program is then solved using the modified L-shaped method. We illustrate our results by an example.     

Production and location on a network under demand uncertainty

The Hakimi theorem is fundamental in location theory. It says that the set of nodes and market-places necessarily contains a profit-maximizing location when the transportation costs are concave in distance. The purpose of this letter is to discuss the validity of this theorem in the context of a two-stage stochastic model of the location of a firm on a network. In the first stage, the firm chooses its location and production level before knowing the exact demands. In the second stage, it observes the realization of the random variables representing the demands and decides upon the distribution of its production. It is shown that the Hakimi theorem still holds in this model when the firm is risk-neutral. On the other hand, in the case of a risk-averse firm, it ceases to be true in that all the points of the network must be considered to obtain an optimal location.     

Sequential entry and exit decisions with an ergodic performance criterion

We consider a variant of an optimisation problem involving sequential entry and exit decisions that has emerged in the economics literature as a real option model. The problem that we solve aims at maximising an ergodic, or long-term average, performance criterion in a pathwise as well as in an expected sense. Such a performance index is probably better suited to decision making within a sustainable economic environment. Our results include a complete characterisation of the optimal strategy, which can take qualitatively different forms depending on the problem's data, as well as explicit expressions for the maximal value of the associated performance index.     

A general framework for cooperation under uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the associated cooperative games are totally balanced. Finally, we consider several example situations.     

Entry and exit of service providers under cost uncertainty: a real options approach

From a real options perspective, this paper examines a service provider's entry and exit decisions toward two types of service outsourcing contracts under service transaction cost uncertainties. Specifically, for a service contract with a flexible duration, the service provider has an option to terminate the contract at any time point by paying a pre-determined exit penalty. For a contract with a fixed-duration, the service provider is obligated to deliver services for a pre-determined period of time. Under this framework, this study seeks to derive the transaction cost conditions that trigger the service provider’s exercise of entry and exit options. Furthermore, via analytical and numerical examinations, this study also uncovers how service transaction cost uncertainty and other business factors (eg, exit penalty and contract duration) influence the service provider’s entry and exit decisions as well as the choice of contract type (ie, fixed-duration versus flexible-duration).     

The impact of price skimming on supply and exit decisions

Stochastic inventory control theory has focused on the order and/or pricing policy when the length of the selling period is known. In contrast to this focus, we examine the optimal length of the selling period—which we refer to as market exit time—in the context of a novel inventory replenishment problem faced by a supplier of a new, trendy, and relatively expensive product with a short life cycle. An important characteristic of the problem is that the supplier applies a price skimming strategy over time and the demand is modeled as a nonhomogeneous Poisson process with an intensity that is dependent on time. The supplier's problems of finding the optimal order quantity and market exit time, with the objective of maximizing expected profit, is studied. Procedures are proposed for joint optimization of the objective function with respect to the order quantity and the market exit time. Then, the effects of the order quantity and market exit time on the supplier's profitability are explored on the basis of a quantitative investigation. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal scheduling of inspection times in a production process with a finite planning horizon

Inspection models applicable to a finite planning horizon are developed for the following lifetime distributions: uniform, exponential, and Weibull distribution. For a given lifetime distribution, maximization of profit is used as the sole optimization criterion for determining an optimal planning horizon over which a system may be operated as well as ideal inspection times. Illustrative examples (focusing on the uniform and Weibull distributions and using Mathematica programs) are given. For some situations, evenly spreading inspections over the entire planning horizon are seen to result in the attainment of desirable profit levels over a shorter planning horizon. Scope for further research is given as well. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal variance stopping with linear diffusions

We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in a general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.     

Planning under uncertainty using parallel computing

Industry and government routinely solve deterministic mathematical programs for planning and schelduling purposes, some involving thousands of variables with a linear or non-linear objective and inequality constraints. The solutions obtained are often ignored because they do not properly hedge against future contingencies. It is relatively easy to reformulate models to include uncertainty. The bottleneck has been (and is) our capability to solve them. The time is now ripe for finding a way to do so. To this end, we describe in this paper how large-scale system methods for solving multi-staged systems, such as Bender's Decomposition, high-speed sampling or Monte Carlo simulation, and parallel processors can be combined to solve some important planning problems involving uncertainty. For example, parallel processors may make it possible to come to better grips with the fundamental problems of planning, scheduling, design, and control of complex systems such as the economy, an industrial enterprise, an energy system, a water-resource system, military models for planning-and-control, decisions about investment, innovation, employment, and health-delivery systems.     

An entry-exit model involving construction and abandonment periods

We analyze, using the optimal stopping theory, the entry-exit decision on a project, which takes time to be constructed and abandoned. We obtain the closed-form expressions of optimal start time of entry, optimal start time of exit, and the maximal expected present value of the project. In addition, we examine the effects of construction and abandonment periods on the optimal start times of entry and exit.     

First exit times for compound Poisson dams with a general release rule

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam.     

Generalized linear fractional programming under interval uncertainty

Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver.     

Robust portfolio selection with uncertain exit time using worst-case VaR strategy

To deal with the robust portfolio selection problem where only partial information on the exit time distribution and on the conditional distribution of portfolio return is available, we extend the worst-case VaR approach and formulate the corresponding problems as semi-definite programs. Moreover, we present some numerical results with real market data.     

Two-product inventory management with fixed costs and supply uncertainty

This paper determines the optimal ordering policy for a two-product, periodic-review inventory problem in which the probability of supply availability is unknown. Moreover, there are two different fixed costs assigned to each product. Demand rates are random variables with known probability density functions, and the supply availability for each product is updated at the beginning of each time period. We prove the optimality of (s,S) policy with a monotone switching curve that indicates the priority of production, where the order-up-to levels and the reorder points are functions of supply availability information. A simple computation is proposed to calculate the two threshold levels. Bayesian updating helps to manage the optimal ordering policy by updating supply disruption information. Numerical results show that improving the accuracy of the forecast leads to making a better ordering decision and eliminating the negative effect of supply disruption on the total cost.     

Portfolio optimization with linear and fixed transaction costs

We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. For such problems, the globally optimal portfolio can be computed very rapidly. Portfolio optimization problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex optimization. We describe a relaxation method which yields an easily computable upper bound via convex optimization. We also describe a heuristic method for finding a suboptimal portfolio, which is based on solving a small number of convex optimization problems (and hence can be done efficiently). Thus, we produce a suboptimal solution, and also an upper bound on the optimal solution. Numerical experiments suggest that for practical problems the gap between the two is small, even for large problems involving hundreds of assets. The same approach can be used for related problems, such as that of tracking an index with a portfolio consisting of a small number of assets.     

Asymmetric risk measures and tracking models for portfolio optimization under uncertainty

Traditional asset allocation of the Markowitz type defines risk to be the variance of the return, contradicting the common-sense intuition that higher returns should be preferred to lower. An argument of Levy and Markowitz justifies the mean/variance selection criteria by deriving it from a local quadratic approximation to utility functions. We extend the Levy-Markowitz argument to account for asymmetric risk by basing the local approximation onpiecewise linear-quadratic risk measures, which can be tuned to express a wide range of preferences and adjusted to reject outliers in the data. The implications of this argument lead us to reject the commonly proposed asymmetric alternatives, the mean/lower partial moment efficient frontiers, in favor of the risk tolerance frontier. An alternative model that allows for asymmetry is the tracking model, where a portfolio is sought to reproduce a (possibly) asymmetric distribution at lowest cost.