Models for investment capacity expansion

The objective of this thesis is to develop and analyse two stochastic control problems arising in the context of investment capacity expansion. In both problems the underlying market fluctuations are modelled by a geometric Brownian motion. The decision maker’s aim is to determine admissible capacity expansion strategies that maximise appropriate expected present-value performance criteria. In the first model, capacity expansion has price/demand impact and involves proportional costs. The resulting optimisation problem takes the form of a singular stochastic control problem. In the second model, capacity expansion has no impact on price/demand but is associated with fixed as well as proportional costs, thus resulting in an impulse control problem. Both problems are completely solved and the optimal strategies are fully characterised. In particular, the value functions are constructed explicitly as suitable classical solutions to the associated Hamilton-Jacobi-Bellman equation

Análisis del control de existencias, en la empresa EMAPAVIGS S.A., Nasca 2021

La presente investigación tuvo como principal objetivo, evaluar el control de existencias en sus fases de ingreso, almacenamiento y salida de mercadería en la Empresa EMAPAVIGS S.A.; para tal efecto se valió de una metodología de tipo descriptivo, con diseño no experimental, por medio de la aplicación de una encuesta a través de un cuestionario como instrumento, el cual fue dirigido a los colaboradores de la empresa, quienes forman la población en este estudio. En los resultados se percibe una adecuada ejecución de las actividades y medidas de prevención en los puntos críticos, puesto que el análisis estadístico muestra una percepción absoluta en un 100% calificando todo el proceso como Eficiente, a su vez el proceso de ingreso de mercadería es calificado en un 100,00% como eficiente, mientras que el proceso de almacenamiento es calificado como eficiente en un 83.33%; asimismo, el proceso de salida de mercadería es calificado de forma eficiente en un 91.67%. Finalmente se concluye que, la empresa tiene deficiencias, en la falta de planificación durante su almacenamiento y salida de los mismos, aduciendo que existe falta de controles en su mercadería, cuyos puntos débiles se tiene que ir mejorando para llegar a una mejora y optimización de control de existencias

An Impulse-Regime Switching Game Model of Vertical Competition

We study a new kind of non-zero-sum stochastic differential game with mixed impulse/switching controls, motivated by strategic competition in commodity markets. A representative upstream firm produces a commodity that is used by a representative downstream firm to produce a final consumption good. Both firms can influence the price of the commodity. By shutting down or increasing generation capacities, the upstream firm influences the price with impulses. By switching (or not) to a substitute, the downstream firm influences the drift of the commodity price process. We study the resulting impulse--regime switching game between the two firms, focusing on explicit threshold-type equilibria. Remarkably, this class of games naturally gives rise to multiple Nash equilibria, which we obtain via a verification based approach. We exhibit three types of equilibria depending on the ultimate number of switches by the downstream firm (zero, one or an infinite number of switches). We illustrate the diversification effect provided by vertical integration in the specific case of the crude oil market. Our analysis shows that the diversification gains strongly depend on the pass-through from the crude price to the gasoline price

Análisis del control de existencia en la Empresa C & Y CORP S.A.C. Callao, 2021

El presente estudio buscó analizar el control de existencias en la empresa C & Y CORP S.A.C en el año 2021; para este cometido se utilizó una metodología de enfoque cuantitativo, nivel explicativo y diseño no experimental, en cuanto a la recolección de datos se utilizó como la encuesta como técnica y el cuestionario como instrumento, el mismo que fue analizado según los requisitos de validez (V Aiken = 100%) y confiabilidad (alfa de Crombach = 0.805). La muestra no probabilística estuvo constituida por 18 colaboradores. Los resultados denotan que el control de existencias de la empresa no es el adecuado; la calificación de la ejecución de la actividades concernientes al proceso en general fue de Regular (73.3%) a Deficiente (38.9%); con relación a los componentes del proceso, la fase de ingreso, almacenamiento y salida de existencias en la empresa es regular en 73.3%, 86.7% y 93.3% de forma respectiva; en conclusión es necesario la intervención de acciones correctivas que mejoren el sistema, como la capacitación del personal en temas referentes a el manejo de Stocks y locación, así como la implementación de políticas que rijan un protocolo de salida, así como la asistencia de algún sistema de registro

Study of new models for insider trading and impulse control

This thesis presents the development and study of two stochastic models. The first one is an equilibrium model for a market involving risk-averse insider trading. In particular, the static information model is considered under new assumptions: a) the insider is risk-averse, b) the signal received by the insider is not necessarily Gaussian, and c) the price set by the market maker is a function of a weighted signal that is not necessarily Gaussian either. Conditions on the weighting and pricing functions ensuring the existence of equilibrium are discussed. Equilibrium pricing and weighting functions as well as the insider’s optimal trading strategy are derived. Furthermore, the influence of the risk aversion on the equilibrium outcome is investigated. The second model studied, we derive the explicit solution to an impulse control problem with non-linear penalisation of control expenditure. This solution has several features that are not present in impulse control problems with affine penalisation of control effort. The state dependence of the free-boundaries characterising the optimal strategy is the first one. The possibility for the so-called continuation region to not be an interval and the optimal strategy to involve multiple simultaneous jumps while the problem data is convex are further such aspects

Análisis del control de existencias, en la empresa Inversiones JEKY SAC, 2023

El presente estudio buscó determinar el nivel control de existencias en la empresa Jeky, 2023, a través de una metodología de enfoque cuantitativo de nivel descriptivo y diseño no experimental, con aplicación de la encuesta y el cuestionario como técnica e instrumento de recolección, aplicado en una muestra no probabilística de 25 trabajadores inmersos en las actividades sobre el manejo de las existencias en la empresa en mención, tal cuestionario fue validado y medido en su confiabilidad aceptable. Los resultados determinan que el control en general es de un nivel medio (76%) a alto (24%), en la misma tendencia para la fase de ingreso; para la fase de almacenamiento se obtuvo un nivel medio (84%) a alto (16%) y para la fase de salida se obtuvo un nivel medio (52%) a al to (48%). Se concluye que el control de existencias de la empresa Jeky SAC es funcional, pero que necesita mejorar algunas actividades que optimicen su proceso, siendo las más importantes aquellas relacionadas a la capacitación del personal y la implementación de normativa, infraestructura y tecnología especializada para el almacenamiento de los productos

Computational methods for stochastic control problems with applications in finance

textStochastic control is a broad tool with applications in several areas of academic interest. The financial literature is full of examples of decisions made under uncertainty and stochastic control is a natural framework to deal with these problems. Problems such as optimal trading, option pricing and economic policy all fall under the purview of stochastic control. These problems often face nonlinearities that make analytical solutions infeasible and thus numerical methods must be employed to find approximate solutions. In this dissertation three types of stochastic control formulations are used to model applications in finance and numerical methods are developed to solve the resulting nonlinear problems. To begin with, optimal stopping is applied to option pricing. Next, impulse control is used to study the problem of interest rate control faced by a nation's central bank, and finally a new type of hybrid control is developed and applied to an investment decision faced by money managers.Information, Risk, and Operations Management (IROM

Stochastic Clearing Models with Applications in Shipment Consolidation

This dissertation focuses on the average cost and service performance models in the shipment consolidation setting, which is treated as an application of stochastic clearing models. Specifically, we consider generalized control policies, generalized demand pattern, multi-item systems, and alternative performance criteria, where various techniques in stochastic analysis and stochastic optimal control are applied. By using stochastic impulsive control technique, we prove that, in the single item shipment consolidation model with drifted Brownian motion demand, the optimal quantity-based policy achieves the least average cost in the long run, among the admissible policies. In multi-item shipment consolidation model, we propose a (Q+τ ) policy and an instantaneous rate policy. We prove that among all (Q + τ ) policies, either a quantity-based policy or a time-based policy is optimal in terms of average cost. Furthermore, we demonstrate that the optimal instantaneous rate policy would dominate the optimal (Q + τ ) policy in terms of average cost. In terms of service performance criteria, we propose average order delay in the single-item case and average weighted delay rate in the multi-item case. From a martingale point of view, we provide a unified method to calculate the service measures. Moreover, by revealing new properties of truncated random variables, we provide comparative results among different control policies in terms of the service measures. Finally, we provide an analytical integrated inventory/hybrid consolidation model, and give comparative results in the integrated inventory/shipment consolidation models in terms of service measures and average cost