Product innovation with partial capacity rollover

Central European Journal of Operations Research - This paper analyzes how the transferability of production capacities from an established to a new product influences the incentives of a firm to...     

The determination of optimal partial fill policy for an inventory system with lumpy demand items

This paper presents a mathematical model developed for the synthesis of optimal replenishment policies for items that experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff point of w units is introduced such that the system would only satisfy routinely customer orders with transaction sizes less than or equal to w units. For customer orders with transaction sizes larger than w units, the system would only supply the cutoff amount (w units). The excess units would be refused. The control discipline is the (s, S) inventory policy with continuous review, and the nature of the customer orders is approximated by a discrete stuttering Poisson distribution. The optimal values of the control parameters, w, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.     

A model for heuristic coordination of real life distribution inventory systems with lumpy demand

This paper presents an approximation model for optimizing reorder points in one-warehouse N-retailer inventory systems subject to highly variable lumpy demand. The motivation for this work stems from close cooperation with a supply chain management software company, Syncron International, and one of their customers, a global spare parts provider. The model heuristically coordinates the inventory system using a near optimal induced backorder cost at the central warehouse. This induced backorder cost captures the impact that a reorder point decision at the warehouse has on the retailers’ costs, and decomposes the multi-echelon problem into solving N + 1 single-echelon problems. The decomposition framework renders a flexible model that is computationally and conceptually simple enough to be implemented in practice.     

Optimal investment with two-factor uncertainty

This paper presents a real options model to value the option to invest in a project contingent on two stochastic factors. A general sensitivity analysis is conducted highlighting the importance of the variance and correlation between the two variables. A higher correlation is shown to increase always the values of the trigger, the active project and the option. The impact of uncertainty is more complex and depends on the assumption about which variables adjust and the correlation between the variables and the market.     

Loss aversion with multiple investment goals

This paper presents a time-continuous portfolio selection model with loss averse investors, who possess multiple investment goals at different time horizons. The model assumes partial narrow framing. Investors follow a two-step approach. First, they optimally allocate wealth among investment goals. Second, they determine an optimal investment strategy for each investment goal separately. We show that when loss aversion is according to the experimental findings, investors mainly invest their wealth to reach long-term goals and adopt investment strategies with high leverage to reach short-term goals. The overall strategy also display high leverage. The same patterns is observed when loss aversion is extreme and goals are very ambitious. By contrast, when loss aversion is extreme but goals are not too ambitious, investors mainly invest to reach short-term goals and adopt safe investment strategies for this purpose.     

The periodic risk model with investment

We consider a periodic risk model with the possibility of investing into a risky asset, given by a geometrical Brownian motion. The aim is to maximize the adjustment coefficient of the risk process. It is shown that the optimal investment strategy only depends on the averaged data of the model and is constant over time. Thus maximizing the adjustment coefficient is a very weak optimization criterion.     

Optimal growth with investment enhancing labor

We study a non-convex optimal growth problem with investment enhancing labor. We prove that there exists an optimal growth path, that all optimal paths are interior and we provide a condition under which at least one of them is monotonic. We also study the existence and uniqueness of the steady state. We show in particular that a rise in the efficiency of the investment enhancing labor does not necessarily lead to an increase in the steady state value of this labor. Furthermore we provide a complete study of the dynamics of the optimal solution in the special case of a logarithmic utility function and a Cobb–Douglas production function.     

A firm's control with price and investment

We consider a dynamic sales and output capacity model. The price function and the investment rate are control variables of a control model that can be solved by synthesis of optimal control paths. This model is similar to a differential game byLevine/Thepot. One of the extensions is that the investment effectiveness function is concave. Two possible optimal strategies can be derived beginning with a positive inventory level and ending with excess capacity, equal sales and output.

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Zusammenfassung Wir beschäftigen uns mit einem dynamischen Absatz- und Outputkapazitäts modell. Preis und Investitionsrate sind Steuervariable eines Kontrollmodells, das durch Verknüpfung von optimalen Pfaden gelöst werden kann. Dieses Modell baut auf einem Differentialspiel vonLevine/Thepot auf. Eine der Erweiterungen besteht darin, daß die Funktion der Investitions effektivität als konkav angenommen wird. Es können zwei mögliche optimale Strategien abgeleitet werden, die mit einem positiven Lagerstand beginnen und mit aufeinander abgestimmten Absatz- und Produktionskapazitäten enden.

     

Optimal investment with deferred capital gains taxes

We solve the optimal portfolio problem of an investor in a complete market who is liable to deferred taxes due on capital gains, irrespective of their origin. In a Brownian framework we explicitly determine optimal strategies. Our analysis is based on a modification of the standard martingale method applied to the after-tax utility function, which exhibits a kink at the level of initial wealth, and Clark’s formula. Numerical results show that the Merton strategy is close to optimal under taxation.     

Optimal investment strategies with a reallocation constraint

We study a Merton type optimization problem under a reallocation constraint. Under this restriction, the stock holdings can not be liquidated faster than a certain rate. This is a common restriction in certain type of investment firms. Our main objective is to study the large time optimal growth rate of the expected value of the utility from wealth. We also consider a discounted infinite horizon problem as a step towards understanding the first problem. A numerical study is done by solving the dynamic programming equations. Under the assumption of a power utility function, an appropriate dimension reduction argument is used to reduce the original problem to a two dimensional one in a bounded domain with convenient boundary conditions. Computation of the optimal growth rate introduces additional numerical difficulties as the straightforward approach is unstable. In this direction, new analytical results characterizing the growth rate as the limit of a sequence of finite horizon problems with continuously derived utility are proved.     

Optimal investment and consumption with stochastic dividends

We use the statistical model of bandit processes to formulate and solve two kinds of optimal investment and consumption problems. The payoffs from the investment are dividend payments with fixed return rates, but the payment frequency is stochastic following a Poisson distribution. The financial market consists of assets which follow Poisson distributions with known or unknown intensity rates. Two kinds of consumption patterns are defined and the optimality of the myopic strategy, the Gittins index strategy, and the play‐the‐winner strategy are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic investment policy with installation experience effects

This paper analyzes the consequences of incorporating a learning-by-doing effect in the firm's adjustment cost function. The hypothesis is that, the larger the existing capital stock, the larger the installation experience gained, and therefore the smaller the cost of installing an additional unit of capital stock. The implications of the hypothesis are investigated in an optimal control model for the determination of the firm's optimal investment policy over an infinite planning period.The research of the second author was sponsored by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

具有随机工资的养老金最优投资问题

在三种目标函数下, 研究了具有随机工资的养老金最优投资问题. 第一种是均值-方差准则, 第二种基于效用的随机微分博弈, 第三种基于均值-方差准则的随机微分博弈. 随机微分博弈问题中博弈的双方为养老金计划投资者和金融市场, 金融市场是博弈的虚拟手. 应用线性二次控制理论求得了三种目标函数下的最优策略和值函数的显式解.     

Nonlinear autoregressive models with heavy-tailed innovation

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.     

The impact of investment lags on investment decision

This paper suggests a valuation framework for an investment project through the concept of real options. Generally, in real asset world, decision time and its payment time are not identical. This so-called investment lag problem should be considered when valuing real assets. When investment lags exist, firms’ accommodation capacities play important roles. In this paper, the real effect of investment lag on investment value is tested upon various conditions. We show the valuation process of real assets under the risk-neutral world. The closed-form formula is also provided for valuing real assets, including R&D project.     

Optimal consumption and investment with insurer default risk

We solve the optimal consumption and investment problem in an incomplete market, where borrowing constraints and insurer default risk are considered jointly. We derive in closed-form the optimal consumption and investment strategies. We find two main results by quantitative analysis. As insurer default risk increases, the proportion of wealth invested in stocks could increase when wealth is small, and decrease when wealth is large. As risk aversion increases, the voluntary annuity demand could increase when insurer default risk is low, and decrease when this risk is high.     

Contrarian investment strategy with data envelopment analysis concept

One of the typical issues in financial literature is that the market tends to be overly pessimistic about value stocks, many of which are past losers. Therefore, over-reactions might capture by measuring earnings surprise vary with past return levels. In this paper, we propose a new index for an effective investment strategy to capture the return-reversal effect using both Data Envelopment Analysis (DEA) and Inverted DEA in order to consider the above characteristics of the market. Our investment strategy using the new index exhibits better performance than the naive return-reversal strategy that only uses past returns or earnings surprise. In addition, the correlations between our new index and commonly used value indices are insignificant, and the value indices cannot represent the over-valued (under-valued) situations perfectly. Hence, considering both proposed and value indices like book-to-price one, we could select value stocks more effectively than by using only one of these indices.     

Infinite-horizon investment consumption model with a nonterminal bankruptcy

This paper solves a general continuous-time consumption and portfolio decision problem for a single agent for whom there exists, upon bankruptcy, a possibility of recovery from his bankruptcy. The main contribution of the paper is in the modeling of the recovery process. Moreover, it is shown that the model with recovery has a one-to-one correspondence with the model with terminal bankruptcy treated in the literature.This research was supported by Grants SSHRC-410-83-9888 and NSERC-A4619 to the first author and by Grants NSF-DMS-86-01510 and AFOSR-88-0183 to the second author. Comments from E. Presman are gratefully acknowledged.     

Dynamic investment strategies with demand-side and cost-side risks

Investments in cost reductions are critical for the long run success of companies that operate in dynamic and stochastic market environments. This paper studies optimal investment in cost reductions as a real option under the assumption that a single firm faces two different sources of risk, stochastic demand and input prices. We derive optimal investment strategies for a monopoly as well as a firm in a perfectly competitive market and show that in case of high marginal costs, cost reductions take place earlier in competitive than in monopoly markets. While the existence of an option to invest in cost reductions increases firm value it also increases a firm’s systematic risk. Risk can be smaller in a monopolistic than in a competitive industry.     

Irreversible investment with random delay and partial prepayment

Classical irreversible investment problem admits an optimal strategy of threshold type. But there is no consensus on how the investor should adjust the threshold, if there is an implementation delay. By formulating a general problem with random delay and partial prepayment, we find that the effect of delay can be opposite for different prepayment rates. Besides, although the constant delay model is commonly used, we argue that it is a reasonable approximation only if the discount rate is small.