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This paper provides some theoretical foundations for using moving average (MA) rules in the stock market. In particular, the paper analyzes the conditional probability of price increments and examines how this probability varies over time. We prove under certain assumptions that the probability of being in an uptrend is greater than the probability of being in a downtrend. This demonstration partially justifies the common use of MA rules in the stock market. Finally, we propose an ex-post empirical analysis to evaluate and compare the performance of some MA rules and other portfolio strategies in the US stock market. In this context, we also suggest a methodology that incorporates these trading rules as alarm rules to predict potential market failures. Our ex-post results confirm the advantages of using these trading rules to predict market trends and crises.

In this paper, we study competition and coordination issues in a duopoly distribution channel where two boundedly rational agents compete on their retail price and warranty policy. The paper analyses the dynamics of competition for three different possible cases where retailers compete: (i) exclusively on price, (ii) exclusively on warranty duration and (iii) both on price and warranty duration. We show that price and warranty competition are dynamically stable in nature under certain condition(s). In such cases, each competition model converges to an equilibrium. However the speed of the parameter adjustment determines how quickly the dynamic game will reach equilibrium and the paper analyses the stability of such an equilibrium. The model is illustrated through a numerical study and the results show that though coordination enhances system profit, it may affect the consumers with higher product price and lower warranty duration. Hence, in some cases, competition serves the firms better than coordination, particularly in terms of ‘social welfare’.

The extent to which central banks are able to anticipate the effects of monetary policy can be assessed within the framework of the liquidity-preference proposition. An actuarial-based theory of liquidity preference is developed in this paper, which extends the traditional framework by introducing borrowing restrictions. This setting can be applied to describe a broad range of corporate, financial and economic decisions. A major result of the paper is that the interest rate elasticity of the money demand, and hence, the effectiveness of monetary policy, directly depends on the series of nominal output returns. Some states are characterized in particular, when the money demand is perfectly elastic and monetary policy is useless to deal with output fluctuations. An analysis of the historical data of the economy of the USA is additionally provided, which presents empirical evidence showing that the interest rate elasticity can increase in response to economic fluctuations. It is thus concluded that not only the growth and inflation rates should be taken into consideration when implementing monetary policy - as is currently the case in a majority of countries - but also the statistical description of the series of nominal output returns.

Demand information sharing is used by many organizations to counter the bullwhip effect. A stream of recent papers claims that the upstream member can mathematically infer the demand at the downstream link (downstream demand inference [DDI]) without any formal information sharing mechanism. In this paper, we investigate DDI when non-optimal forecasting methods are employed by supply chains. We show that in the case of a simple moving average forecast, the demand at the downstream link can be inferred. In the case of single exponential smoothing (SES), downstream demand cannot be inferred and thus needs to be shared. Finally, we quantify the value of sharing demand information when SES is employed.

This paper deals with a continuous review, two-echelon serial (two locations) inventory system with perishable items. Transportation times and the lifetime of items are fixed. When the age of an item has reached its lifetime, the item is useless and consequently discarded from the system. The downstream location faces Poisson demand, and demand that cannot be met immediately is backordered. In this paper, we develop an efficient approximate technique for evaluation of (S-1, S) policies. In a simulation study, we evaluate the quality of our approximation. The results reveal that our approximate technique works well in most cases.

In the author's concept of risk-averse maintenance, introduced in a previous paper, we seek to minimize the disutility of cost per unit time rather than to minimize cost per unit time itself. This gives a maintenance policy that is optimal under risk aversion. This paper extends the earlier work by providing a solution to the problem of combining risk aversion with the cost discounting that arises from the time value of money. The effect of parameter uncertainty, which was touched on in the earlier work, is here shown to lead to a minimax solution when operation for a long period with model uncertainty is planned. The possible use of non-exponential utility functions is discussed. In an attempt to make risk-averse maintenance more meaningful for practitioners, a fresh example of its use, the maintenance of a standby system, is given. A graphical aid to decision support is given, and some useful financial measures of risk, value at risk and expected shortfall, are introduced. These can be used to characterize planned maintenance policies.

Control tunnelling over firms can be reached through pyramids, cross-ownership, and other complex features. This phenomenon is frequent in Europe and in Asia. However, the theoretical literature has not yet converged toward a well-defined and robust measurement of integrated control that takes into account the threshold for control as applied in practice. Based on graph theory, this paper aims at filling this gap and proposes a new algorithm for evaluating the control tunnelling exerted by the firms' ultimate shareholders. Then, the paper discusses the various forms of control existing next to voting shares, like multiple voting rights, board representation and active monitoring, before suggesting ways to include them into the modelling of control.

This paper provides the first optimal portfolio analysis for a constant relative risk-averse and ambiguity-averse investor under the state-of-the-art 4/2 stochastic volatility model in a complete market setting. We determine the robust optimal strategy and the worst case measure by allowing separate levels of uncertainty for variance and stock drivers. Technical conditions for well-defined solutions are detailed together with a verification result. The robust optimal investment exposure displays a dependence on current volatility levels similar to the non-robust case further impacted by the ambiguity-aversion level. Using real-world parameters, the numerical analysis finds that wealth-equivalent losses (WELs) from ignoring uncertainty or market completeness are moderate. On the other hand, WELs for investors who follow simpler but popular strategies, such as Heston (1/2 model) and Merton (geometric Brownian motion [GBM] model), could be quite substantial, of up to 24 and 51%, respectively. This latest analysis comes from new non-affine representations for the suboptimal value function of the 1/2 and GBM strategies.

Energy quanto options are risk management tools that have a payoff similar to the product of the payoffs of two options, each written on an energy-related underlying. These options, as opposed to standardized contracts that only account for price risk, are designed to manage both volumetric and price risk in energy markets. Since the use of such options enables actors in the energy market also to hedge against production volume risk, they are becoming very popular. This paper considers the valuation of such an option on futures when the underlying futures prices are governed by Markov-modulated additive processes, which have independent but non-stationary increments within each regime. We derive a valuation formula by using the Fast Fourier Transform (FFT) technique under the assumption that the joint characteristic function of the log-futures prices is known analytically. We study this approximation under different regime-switching models. Several numerical case studies illustrate that our FFT-based valuation has a high precision and is much faster than Monte Carlo estimates.

We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.

In this paper, the pricing of foreign exchange options is considered under a modified Heston–Cox–Ingersoll–Ross hybrid model. This modified model reserves all the characteristics of the Heston–Cox–Ingersoll–Ross model and also additionally assumes regime switching in the key parameters of the volatility as well as the domestic and foreign interest rates. Even though complicated, we have derived a closed-form pricing formula for foreign exchange options after the affinity of this new model is verified. Various properties of the newly derived formula are also shown through numerical experiments. To show the performance of this newly proposed model, an empirical study is also conducted, the result of which suggests that our model is a good alternative to the Heston–Cox–Ingersoll–Ross model for practical purpose.

In quantitative finance practice, model calibration is a key challenge. This is especially so when a local regime-switching model needs to be calibrated because designing an efficient and reliable algorithm to obtain local volatility values as a function of underlying price and time is important for the model to be successfully used in practice. Therefore, this paper proposes a new algorithm for calibrating local regime-switching models with observed option prices available for a particular market that is suitable for this type of model. The newly proposed algorithm is tested with calibrations performed on synthetic as well as real market data. Our empirical test results indicate that the algorithm has great potential to be used in financial risk management.

In this paper, we construct quantitative models in which the dependence structure of the firms’ default times is incorporated. Such models serve as the underlying frameworks in our proposed approach to price and hedge basket credit derivatives. Through the Gaussian copula-based method, we model the default correlation risk and develop valuation formulas for credit derivatives. Using single-name derivatives in a hedging strategy for basket credit derivatives, the utility of the delta and delta-gamma hedging techniques are examined. This enables the management of risk attributed to the changes in correlation without the need for a large number of hedging instruments. Our research contributions provide insights on how dependent risks in basket credit derivatives could be dealt with effectively.

In this paper, the fair price of an American-style resettable convertible bond (CB) under the Black–Scholes model with a particular reset clause is calculated. This is a challenging problem because an unknown optimal conversion price needs to be determined together with the bond price. There is also an additional complexity that the value of the conversion ratio will change when the underlying price touches the reset price. Because of the additional reset clause, the bond price is not always a monotonically increasing function with the underlying price, which is impossible for other types of the CBs. Of course, the problem can be dealt with using the Monte-Carlo simulation. But, a partial differential equation (PDE)/integral equation approach is far superior in terms of computational efficiency. Fortunately, after establishing the PDE system governing the bond price, we are able to present an integral equation representation by applying the incomplete Fourier transform on the PDE system.

The interest rate and the market price of risk may be stochastic in a real-world financial market. In this paper, the interest rate is assumed to be driven by a stochastic affine interest rate model and the market price of risk from the stock market is a mean-reverting process. In addition, the dynamics of the stock are simultaneously driven by random sources of interest rate and the stock market itself. In pension fund management, different fund managers may have different risk preferences. We suppose risk preference is described by the hyperbolic absolute risk aversion utility, which is a general utility function describing different risk preferences. Legendre transform-dual theory is presented to successfully obtain explicit expressions for optimal strategies. A numerical example illustrates the sensitivity of optimal strategies to market parameters. Theoretical results imply that the risks from stochastic interest rate and stochastic return may be completely hedged by adopting specific portfolios.

A credit-linked note (CLN) is a type of credit derivative, constructed with a bond and an embedded credit default swap, which allows the issuer to transfer a specific credit risk to credit investors. In this paper, we model CLNs with and without counterparty risk in the reduced-form framework. For CLNs with counterparty risk, we consider two different scenarios, i.e. the issuer of CLNs and reference assets have either positive correlation or negative correlation. Assuming the interest rate follows the Cox–Ingersoll–Ross (CIR) model (Cox et al., 1985) and the default events mainly depend on the interest rate, we model the two different correlations. Explicit formulas for value functions are obtained through a partial differential equation approach. In addition, counterparty valuation adjustment and the dependence on related parameters are also investigated.

This paper investigates the effects of various forecasting methods, such as moving average (MA), exponential smoothing (ES) and linear regression (LR) on the bullwhip effect in a four-echelon supply chain. In order to compare the effectiveness of these forecasting methods, a bullwhip effect measure is utilized for two cases: one where the demand is non-trended and one where it has an increasing trend. The forecasting methods in these two cases are ranked based on the size of bullwhip effect they cause, and a statistical method is utilized to ascertain the significance of the differences among these effects. The results obtained show that the LR, double MA and double ES methods result in the least, the second least and the largest bullwhip effect, respectively, in the case of trended demand. Moreover, the simple MA, single ES and LR methods cause the least, the second least and the largest bullwhip effect, respectively, in the case of non-trended demand. Finally, the results are generalized for other tree-like supply chains using an analytical representation.

This paper addresses the capital budgeting problem under uncertainty. In particular, we propose a multistage stochastic programming model aimed at selecting and managing a project portfolio. The dynamic uncertain evolution of each project value is modelled by a scenario tree over the planning horizon. The model allows the decision maker to revise decisions by decommitting from a given project if it shows a negative performance. Risk is explicitly assessed by defining a mean-risk objective function, where the conditional value at risk is used. A customized branch-and-bound method is also introduced for solving the proposed model. Extensive computational experiments have been carried out to validate the model effectiveness, also in comparison with other possible benchmark policies. The numerical results collected by solving randomly generated instances with the proposed branch-and-bound approach seems to be encouraging. 15

Thangam & Uthayakumar (2010, Optimal pricing and lot-sizing policy for a two warehouse supply chain system with perishable items under partial trade credit financing. Oper. Res. Int. J., 10, 133–161) investigated perishable items with limited storage capacity under a partial trade credit policy. For simplification, they used Taylor series approximations to derive their solution procedures. In our paper, we develop an exact solution procedure that avoids the problem of assuming that the deterioration rate is small, thereby improving the accuracy of the solution but more fundamentally increasing the practical relevance of the solution.

By employing data on 337 bank-year observations, the paper examines the impact of consolidation on efficiency and competition in the Malaysian banking sector during 1996–2008. We employ the Panzar-Rosse (P-R) H-statistic method to evaluate the degree of competition, while Data Envelopment Analysis (DEA) is employed to compute the efficiency of individual banks. The empirical findings from the DEA suggest that the Malaysian banking sector has been relatively inefficient in their intermediation function during the post-merger period. On the other hand, we find that the Malaysian banking sector has been relatively more efficient during the post-merger period under the revenue approach. The test of market contestability by using the P-R method seems to reject both monopoly and perfect market competition conditions indicating monopolistic market behaviours among banks operating in the Malaysian banking sector.

A number of problems in economics, finance and insurance rely on determining the sign of the covariance of two transformations of a random variable. The classical Chebyshev’s inequality offers a powerful tool for solving the problem, but it assumes that the transformations are monotonic, which is not always the case in applications. For this reason, in the present paper, we establish new results for determining the covariance sign and provide further insights into the area. Unlike many previous works, our method of analysis, which is probabilistic in its nature, does not rely on the classical Hoffding’s representation of the covariance or on any of its numerous extensions and generalizations. We motivate our research with several problems arising in economics, finance and insurance.

Combinatorial auctions allow bidders to bid on individual items or bundles of items. This enables bidders to take advantage of the synergy or complementarity in their valuations of bundles. However, the number of bundles or packages that a bidder could explore may be large making these auctions too complex. Therefore, a combinatorial auction is often run as an iterative auction involving a series of rounds that progressively lead to a final allocation. In each intermediate round, bids are submitted and then provisional winners are determined. A key element in each round is the provision of price feedback to guide bidders in subsequent rounds. This price feedback can focus on packages or on items. Item (also known as linear) pricing feedback schemes have been widely researched for combinatorial auctions on unique items (where packages consist of one or more unique items but not multiple amounts of any item). It has been observed that such item price schemes have performed reasonably well in a wide variety of auction markets. However, they have not yet been thoroughly tested for auctions where the allocation involves multiple units of different items. In this paper, we extend several item pricing designs to the case of multiple unit combinatorial auctions. We identify a set of performance criteria by which an auctioneer could assess the suitability of a design for their particular case. We then numerically compare the algorithms using an agent-based model. Based on the results, we draw some general conclusions about the strengths and limitations of different schemes.

This paper uses the expected utility framework to examine the optimal hedging decision for commodities with mean reverting price processes. The derived results show that when commodity prices follow a mean reverting process, the optimal hedge ratio differs significantly from the classical results found under standard geometric Brownian motion. Hence a failure to accommodate mean reversion when it exists can lead to systematic biases in hedging and investment decisions respectively.

This paper considers an energy-pollution economic problem which uses a stochastic queue framework. This approach is shown to establish a link between a firm's energy consuming economic activity and its effects on the pollution that it generates as a function of its activity. An economic model is then used to draw some inferences regarding the effects of selected economic parameters on the propensity to pollute and prevent pollution. In particular, a number of theories pertaining to the effects of pollution and its regulation on the output and competitiveness of firms is elaborated. For example, the Porter Hypothesis presuming that a stringent environmental policy improves a firm’s competitiveness is analyzed in terms of our model. For demonstration purposes, a simple example is used.

In inventory management, hierarchical forecasting (HF) is a hot issue: families of items are formed for which total demand is forecasted; total forecast then is broken up to produce forecasts for the individual items. Since HF is a complicated procedure, analytical results are hard to obtain; consequently, most literature is based on simulations and case studies. This paper succeeds in following a more theoretical approach by simplifying the problem: we consider estimation instead of forecasting. So, from a random sample we estimate both the total demand and the fraction of this total that individual items take; multiplying these two quantities gives a new estimate of the individual demand. Then, our research question is: Can aggregation of items, followed by fractioning, lead to more accurate estimates of individual demand? We consider two simple situations that can be analysed fully theoretically. Thirdly, a more practical situation is investigated by means of simulation.

In this paper, we consider the demand-forecasting problem of a make-to-stock system operating in a business-to-business environment where some customers provide information on their future orders, which are subject to changes in time, hence constituting imperfect advance demand information (ADI). The demand is highly volatile and non-stationary not only because it is subject to seasonality and changing trends but also because some individual client demands have significant influence on the total demand. In such an environment, traditional forecasting methods may result in highly inaccurate forecasts, since they are mostly developed for the total demand based only on the demand history, not making use of demand information and ignoring the effects of individual order patterns of the customers. We propose a forecasting methodology that makes use of individual ordering pattern histories of the product–customer combinations and the current build up of orders. Moreover, we propose making use of limited judgemental updates on the statistical forecasts prior to the use of ADI.

Demand forecasting and stock control are traditionally examined as independent of each other. Even though this weakness has been highlighted in the academic literature, little empirical work has been conducted on forecasting adjustments addressing the interaction between forecasting and stock control. In this paper, the relevant literature is critically reviewed. Subsequently, the empirical performance of some modifications and adjustments, on slow-moving items, is examined in detail. The data set consists of the individual demand histories of 753 intermittent line items from the Royal Air Force (UK). Overall, the results indicate that there is a scope for improving the performance of parametric stock control systems, and adjustments are indeed required in order to account for the interaction between forecasting and stock control.

A discrete-event simulation model of a supply chain has been developed to evaluate operational performance of sharing uncertain information on upcoming demand between an original equipment manufacturer (OEM) and a contract manufacturer under a formal rolling horizon flexibility (RHF) contract in a four-node supply chain. There are two types of RHF contracts evaluated, i.e. RHF contract with constant flexibility and decreasing flexibility bounds. The demand is externalized (i.e. the OEM receives the demand), stochastic and generated according to a gamma distribution. This paper reports on the analysis of RHF contracts operating with coefficients of variation of demand up to 2.00. Analysis of the interaction of RHF contracts with forecasting and the impact an RHF contract has on the transmission of the bullwhip effect are reported here.

We use regression methods to predict the expected monthly return on stocks and the covariance matrix of returns, the predictor variables being a company's ‘fundamentals’, such as dividend yield and the history of previous returns. Predictions are evaluated out of sample for shares traded on the London Stock Exchange from 1976 to 2005. We explore and evaluate many modelling and inferential approaches, including the use of weighted regression, discounted regression, shrinkage of regression coefficients and the transformation to normality of predictor variables. We also investigate alternative covariance matrix models, such as a two-index model and a shrinkage model. Using suitable statistics to enable the out-of-sample performance of competing methodologies to be compared is crucial, and we develop some new statistics and a graphical aid for this purpose. What is original in this paper is an evaluation of many modelling and inferential procedures for which conflicting claims have been made in the literature and the development of new measures of portfolio performance.

This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull–White model. The default barrier is considered as an option writer’s liability. Closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the stochastic default barriers on option values. The numerical results show that negative correlation between the firm values and the stochastic default barriers of option writers gives material reductions in option values where the options are written by firms with leverage ratios corresponding to BBB or BB ratings.

We study an optimal investment problem for a diffusion market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are not necessarily adapted to the driving Brownian motion, and their distributions are unknown, but they are supposed to be currently observable. The optimal investment problem is stated as a problem with a maximin performance criterion which leads to maximization of the minimum of expected utility over all distributions of parameters. We found that including the non-discounted wealth to the utility (in addition to the discounted wealth) implies an additional condition for the saddle point of the maximin problem: it must be a solution of an additional minimization problem for the risk-free return. This is different from the case when the utility depends on the discounted wealth only. Using these results, the maximin problem is reduced to a linear parabolic equation and minimization (over two scalar parameters). It is an important addition to the result obtained in the author's paper (2006).

The recent movement towards an open, competitive market environment introduced new optimization problems such as market clearing mechanism, bidding decision and Available Transfer Capability (ATC) calculation. These optimization problems are characterized by the complexity of power systems and the uncertainties in the electricity market. Accurate evaluation of the transfer capability of a transmission system is required to maximize the utilization of the existing transmission systems in a competitive market environment. The transfer capability of the transmission networks can be limited by various system constraints such as thermal, voltage and stability limits. The ability to incorporate such limits into the optimization problem is a challenge in the ATC calculation from an engineering point of view. In the competitive market environment, a power supplier needs to find an optimal strategy that maximizes its own profits under various uncertainties such as electricity prices and load. On the other hand, an efficient market clearing mechanism is needed to increase the social welfare, i.e. the sum of the consumers’ and producers’ surplus. The need to maximize the social welfare subject to system operational constraints is also a major challenge from a societal point of view. This paper presents new optimization techniques motivated by the competitive electricity market environment. Numerical simulation results are presented to demonstrate the performance of the proposed optimization techniques.

This paper compares the predictive performance of linear discriminant analysis, neural networks, genetic algorithms and decision trees in distinguishing between good and slow payers of bank credit card accounts. Predictive models were built using the evolutionary techniques and the results compared with those gained from the discriminant analysis model published in Crook et al. (1992), The Service Industries Journal 12 which uses the same dataset. A range of parameters under the control of the investigator was investigated. We found that the predictive performance of linear discriminant analysis was superior to that of the other three techniques. This is consistent with some studies but inconsistent with others.

Statistical measures of risk based on historical data are useful tools in assessing risk for conventional investment-trust securities; but they are of limited use for securities of split-capital investment trusts, and an alternative approach is proposed in this paper. By differentiating formulae for the discounted cash flow, with respect to the underlying fundamental variables, ‘sensitivity measures’ can be derived for most securities of split-capital investment trusts. These sensitivity measures show how the present value of expected future cash flows will vary as the real discount force changes, the real force of increase in the income (or capital value) of the underlying fund changes, and the estimated force of inflation changes.

Accountants seeking to estimate the profitability of a firm via the calculation of earnings utilize information about the number and current lifespan of unfinished activities by incorporating a smoothing device—depreciation—into their calculations. This paper considers a firm in steady state, carrying out a large number of similar activities with random starts and completion dates. By developing a stochastic model for the firm's activities, a difference equation for the minimum-variance smoothing function is obtained. This can be solved explicitly in the case of a periodic Poisson process of start times and independent exponential durations and is a variant of declining-balance depreciation.

In this paper we propose using computational tests for appraising the inaccuracies of index numbers (for example, price and wage indices). This is done by programming a hypothetical situation where the true average index value is known and the variation of prices and quantities and the relation between them can be chosen. The indices are then calculated using the formulae of Laspeyres, Paasche, Fisher, the Unit index and Normalized Unit index formulae. By comparing the average values of the above formulae with the true average index value, we are able to obtain a quantitative indication of the errors in these formulae under various situations. The Normalized Unit and Fisher index formulae were found to be consistently accurate for all our tests whereas the formulae of Laspeyres and Paasche were found to have very poor accuracy in the majority of our tests. The Unit index was also consistently accurate in all our tests but its use is appropriate in the single item case thus making this formula suitable for measuring wages. In our informal discussion of stability we indicated that the Normalized unit index and the Unit index have good stability characteristics whereas the indices Laspeyres, Paasche and Fisher have poor stability characteristics. In view of the above the Normalized Unit index is the best of the formulae we have discussed for measuring prices (many item case), and the Unit index is the best of the formulae we have discussed for measuring wages (single item case).