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STOCHASTIC MODELS ABSTRACTS
ALAIN BENSOUSSAN, University of Texas at Dallas - School of Management In many businesses, inventory levels are only incompletely observed. This may be due to non-observation, of demand, spoilage, misplacement, or theft of inventory. The non-observation of demand may be caused, e.g., by transaction errors or by discrepancies/delays in transmitting/processing sales data. We study a periodic review inventory system where the demand is not observed and the unmet demand is backordered. As a result, the inventory manager cannot tell the exact quantities of inventories or backorders. However, by looking at the shelf, he knows whether the inventory is positive or non-positive. Only with this information, the inventory manager must determine the order quantity in each period that would minimize the expected total discounted cost over an infinite-horizon. The dynamic programming formulation of this problem has an infinite-dimensional state space. We use the concept of unnormalized probability to establish the existence of an optimal feedback policy and the uniqueness of the solution of the dynamic programming equation when the periodic cost has linear growth. "Bayesian Model Selection for Structural Break Models"
ANDREW T. LEVIN, Federal Reserve Board We take a Bayesian approach to model selection in regression models with structural breaks in conditional mean and residual variance parameters. A novel feature of our approach is that it does not assume knowledge of the parameter subset that undergoes structural breaks, but instead conducts model selection jointly over the number of structural breaks and the subset of the parameter vector that changes at each break date. Simulation experiments demonstrate that conducting this joint model selection can be quite important in practice for the detection of structural breaks. We apply the proposed model selection procedure to characterize structural breaks in the parameters of an autoregressive model for post-war U.S. inflation. We find important changes in both residual variance and conditional mean parameters, the latter of which is revealed only upon conducting the joint model selection procedure developed here.
LUZ R. SOTOMAYOR, University of Alberta - Department of Mathematical and Statistical Sciences Motivated by economic and empirical arguments, we consider a company whose cash reservoir is affected by macroeconomic conditions. Specifically, we model the cash reservoir as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study three different cases: bounded dividend rates, unbounded dividend rates, and the case in which there are fixed costs and taxes associated to the dividend payments. These cases generate, respectively, problems of classical stochastic control with regime switching, singular stochastic control with regime switching,and stochastic impulse control with regime switching (a new problem in the stochastic control literature). We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. Our results shows, among other things, that the optimal dividend policy depends strongly on macroeconomic conditions. "American Options in Lévy Models with Stochastic Interest Rates"
SVETLANA BOYARCHENKO, University of Texas at Austin - Department of Economics A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Lévy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. An explicit algorithm for the case of positive stochastic interest rates driven by a process of the Ornstein-Uhlenbeck type is derived. Efficiency of the method is illustrated with numerical examples. | |||||||||
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Solicitation of Abstracts
This abstracting journal distributes working and accepted papers that propose models, perform analysis, and develop analytical, computational or statistical methods for stochastic systems where variability plays a central role. The journal welcomes research with a focus on applications in functional areas, such as financial engineering, manufacturing, service and supply chain operations, revenue and yield management, telecommunications and networking, where the contributions transcend its functional context. Topics of interest include, but are not limited to, work that provides substantial structural insights via the analysis of tractable yet reasonable models of stochastic systems, work that is intended for literal implementation of policy prescriptions based on computational methods, and work that is for empirically estimating essential parameters used in statistical methods for control and optimization.
Distribution ServicesIf your Institution is interested in learning more about increasing readership for its research by becoming a Partner in Publishing or starting a Research Paper Series, please email: PIP@SSRN.com. Distributed by:
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