Efficiency and marginal cost pricing in dynamic competitive markets with friction

This paper examines a dynamic general equilibrium model with supply friction. With or without friction, the competitive equilibrium is efficient. Without friction, the market price is completely determined by the marginal production cost. If friction is present, no matter how small, then the market price fluctuates between zero and the "choke-up" price, without any tendency to converge to the marginal production cost, exhibiting considerable volatility. The distribution of the gains from trading in an efficient allocation may be skewed in favor of the supplier, although every player in the market is a price taker.Dynamic general equilibrium model with supply friction, choke-up price, marginal production cost, welfare theorems

Controlled diffusion processes

This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points

A single machine produces several different classes of items in a make-to-stock mode. We consider the problem of scheduling the machine to regulate finished goods inventory, minimizing holding and backorder or holding and lost sales costs. Demands are Poisson, service times are exponentially distributed, and there are no delays or costs associated with switching products. A scheduling policy dictates whether the machine is idle or busy, and specifies the job class to serve in the latter case. Since the optimal solution can only be numerically computed for problems with several products, our goal is to develop effective policies that are computationally tractable for a large number of products. We develop index policies to decide which class to serve, including Whittle's "restless bandit" index, which possesses a certain asymptotic optimality. Several idleness policies, which are characterized by hedging points, are derived, and the best policy is obtained from a heavy traffic diffusion approximation. Nine sample problems are considered in a numerical study, and the average suboptimality of the best policy is less than 3%

An optimal trading problem in intraday electricity markets

We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and on the intraday price, typically due to error in the prediction of wind power generation. Finally, we solve the problem when taking into account delay constraints in thermal power production.Comment: 39 pages, 11 figure

Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section

An analysis of spending behaviour under liquidity constraints with an application to financial hedging

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Revenue Management for Make-to-Order and Make-to-Stock Systems

With the success of Revenue Management (RM) techniques over the past three decades in various segments of the service industry, many manufacturing firms have started exploring innovative RM technologies to improve their profits. This dissertation studies RM for make-to-order (MTO) and make-to-stock (MTS) systems. We start with a problem faced by a MTO firm that has the ability to reject or accept the order and set prices and lead-times to influence demands. The firm is confronted with the problem to decide, which orders to accept or reject and trade-off the price, lead-time and potential for increased demand against capacity constraints, in order to maximize the total profits in a finite planning horizon with deterministic demands. We develop a mathematical model for this problem. Through numerical analysis, we present insights regarding the benefits of price customization and lead-time flexibilities in various demand scenarios. However, the demands of MTO firms are always hard to be predicted in most situations. We further study the above problem under the stochastic demands, with the objective to maximize the long-run average profit. We model the problem as a Semi-Markov Decision Problem (SMDP) and develop a reinforcement learning (RL) algorithm-Q-learning algorithm (QLA), in which a decision agent is assigned to the machine and improves the accuracy of its action-selection decisions via a “learning process. Numerical experiment shows the superior performance of the QLA. Finally, we consider a problem in a MTS production system consists of a single machine in which the demands and the processing times for N types of products are random. The problem is to decide when, what, and how much to produce so that the long-run average profit. We develop a mathematical model and propose two RL algorithms for real-time decision-making. Specifically, one is a Q-learning algorithm for Semi-Markov decision process (QLS) and another is a Q-learning algorithm with a learning-improvement heuristic (QLIH) to further improve the performance of QLS. We compare the performance of QLS and QLIH with a benchmarking Brownian policy and the first-come-first-serve policy. The numerical results show that QLIH outperforms QLS and both benchmarking policies