Narrow Results

This paper analyzes an infinite horizon, single-product, continuous-time inventory model with supply and demand risks to evaluate the impact of coordinating a production policy between a distributor and a supplier. We consider a wholesale-price contract and a shortage penalty contract as a coordination mechanisms in an inventory replenishment system. The demand process is described by a Brownian motion with drift, and this inventory model can be formulated as an impulse control problem with uncertain replenishment quantities. We show that under some assumptions, there exist optimal ordering and production policies. We also provide some numerical examples to investigate the effect of these coordination mechanisms on the expected costs and the optimal policies. The computational experiments reveal that (i) the production quantity in decentralized case is higher than that in the centralized case, (ii) the centralized approach strategy results in the lower joint total cost as compared with independent decision approaches, and (iii) the shortage penalty contract has a beneficial effect on the total cost to the entire supply chain in decentralized system.

We study the problem of optimally liquidating a large portfolio position in a limit-order market. We allow for both limit and market orders and the optimal solution is a combination of both types of orders. Market orders deplete the order book, making future trades more expensive, whereas limit orders can be entered at more favorable prices but are not guaranteed to be filled. We model the bid-ask spread with resilience by a jump process, and the market-order arrival process as a controlled Poisson process. The objective is to minimize the execution cost of the strategy. We formulate the problem as a mixed stochastic continuous control and impulse problem for which the value function is shown to be the unique viscosity solution of the associated variational inequalities. We conclude with a calibration of the model on recent market data and a numerical implementation.

We develop a trading strategy that employs limit and market orders in a multiasset economy where the assets are not only correlated, but can also be structurally dependent. To model the structural dependence, the mid-price processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the bid–ask spreads of the assets. We provide a mathematical framework for such an economy and solve for the value function and optimal control for an investor who takes positions in these assets. The optimal strategy exhibits two dominant features which depend on how far the vector of mid-prices is from the no-arbitrage bounds. When mid-prices are sufficiently far from the no-arbitrage edges, the strategy behaves as that of a market maker who posts buy and sell limit orders. And when the mid-price vector is close to the edge of the no-arbitrage region, the strategy executes a combination of market orders and limit orders to profit from statistical arbitrages. We discuss a numerical scheme to solve for the value function and optimal control, and perform a simulation study to discuss the main characteristics of the optimal strategy.

We apply impulse control techniques to a cash management problem within a mean-variance framework. We consider the strategy of an investor who is trying to minimise both fixed and proportional transaction costs, whilst minimising the tracking error with respect to an index portfolio. The cash weight is constantly fluctuating due to the stochastic inflow and outflow of dividends and liabilities. We show the existence of an optimal strategy and compute it numerically.

We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ³ could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on the regions of the state space, this manifold is either a dispersal one, an equivocal one or a 2D focal manifold. A pair of PDE's were derived for the focal part. Here we show that irrespective of the nature of this manifold, it has to satisfy this same set of PDE's.

This study examines an environmental management strategy to effectively cap greenhouse gas (GHG) emissions in an electricity market. To do so, we model a stochastic impulse two-person, nonzero-sum game between a power plant, a representative of electricity production within a country whose primary aim is to maximize profits, and government who is motivated to minimize the social and environmental cost of pollution. We assume that the power plant’s competitive price is equal to the marginal cost whilst the government’s running cost is linear. When the uncontrolled output of GHG emissions evolves as a Geometric Brownian motion, we provide a more dynamic and robust depiction of the interplay between government and the energy sector. We provide solutions to the impulse control problem derived via the quasi-variational inequalities (QVIs). We then present a sufficiency criterion for the existence of a Nash equilibrium for the optimal policy. Ultimately, our use of short-run price competition characterized by strategic supplies for renewable and fossil resources and inclusion of endogenous constraints on production capacity provides a more robust model and an effective framework for the development of policy that allows governments to meet emissions targets whilst guaranteeing energy supply.

Based on the population model with an Allee effect, the corresponding delayed model is built up. According to the qualitative theory of differential equations, the model is analyzed completely to describe various intriguing dynamic properties as singular point of high order, Hopf bifurcation, etc. Next, combined impulse control theory with the ecological principles, the control models with impulse effects are proposed and the corresponding controllers are designed not only to avoid the extinction of the populations but also to prevent outbreak of the populations. The study would not only reveal the complexity dynamic behavior of ecosystems, but also provide the theory reference for the management of populations.

This paper applies the theory of real options and impulse control to information security investment and derives properties of an optimal investment rule. It also incorporates adjustment costs incurred whenever the level of the investment changes. We observe among others that if firm has opportunity of multiple investments, it behaves so cautiously that the timing is earlier and to invest more. Both adjustment costs and volatility of threat make interval of the investment longer, while vulnerability leads to shorter interval and therefore frequent investment.

Technological addiction is a common issue worldwide that has seldomly been investigated; this research has developed a possible path model on further acknowledgment of the problematic use of technology. Present study (N = 211 Chinese adults) has investigated the relationships of parenting styles (PS), attachment style (AS), self-regulation, self-esteem and Smartphone addiction (SA). Results show that PS considerably predicts different types of AS. Secure and anxious AS was desirably predicted self-regulation and self-esteem. Under self-regulation, higher impulse control also successfully predicts less SA, while goal setting negatively predicted SA. The model helps explore new relationships between Smartphone addiction and other constructs in an educational psychology aspect. It also helps gain insight on how parenting and selfregulation influences Smartphone usage. Programs which promote parenting skills and correct regulating skills are suggested.

We study the control band policy arising in the context of cash balance management. A policy is specified by four parameters (d, D, U, u). The controller pushes the process up to D as soon as it goes below d and pushes down to U as soon as it goes above u, while he does not intervene whenever it is within the set (d, u). We focus on the case when the underlying process is a spectrally one-sided Lévy process and obtain the expected fixed and proportional controlling costs as well as the holding costs under the band policy.