1,721,062 research outputs found
Numerical methods in finance and economics: a MATLAB-based introduction (2nd edition)
No full textThe book deals with numerical methods relevant for financial applications, such as portfolio optimization and derivative pricing. After introductory chapters on financial markets and instruments, also covering models based on stochastic differential equations and risk measurement issues, and on numerical methods, we move on to describe the most important tools, such as: 1) numerical integration by Monte Carlo sampling and low-discrepancy sequences (with due emphasis on variance reduction strategies); 2) finite difference methods for partial differential equations; 3) optimization methods. These methods are illustrated, along with MATLAB code, in later chapters describing several applications to option pricing and portfolio optimization. We deal in particular with binomial/trinomial lattices, exotic option pricing by Monte Carlo simulation, finite difference methods for option pricing, portfolio optimization by mixed-integer and stochastic linear programming, and numerical dynamic programming, which is also the foundation of recent methods to price high-dimensional, American-style option
Multi-item capacitated lot-sizing with demand uncertainty
No full textWe consider a stochastic version of the classical multi-item Capacitated Lot-Sizing Problem (CLSP). Demand uncertainty is explicitly modeled through a scenario tree, resulting in a multi-stage mixed-integer stochastic programming model with recourse. We propose a plant-location based model formulation and a heuristic solution approach based on a fix-and-relax strategy. We report computational experiments to assess not only the viability of the heuristic, but also the advantage (if any) of the stochastic programming model with respect to the considerably simpler deterministic model based on expected value of demand. To this aim we use a simulation architecture, whereby the production plan obtained from the optimization models is applied in a realistic rolling horizon framework, allowing for out-of-sample scenarios and errors in the model of demand uncertainty. We also experiment with different approaches to generate the scenario tree. The results suggest that there is an interplay between different managerial levers to hedge demand uncertainty, i.e., reactive capacity buffers and safety stocks. When there is enough reactive capacity, the ability of the stochastic model to build safety stocks is of little value. When capacity is tightly constrained and the impact of setup times is large, remarkable advantages are obtained by modeling uncertainty explicitl
Mean-risk optimization in production planning: an application of stochastic programming to an assembly-to-order problem.
No full textHandbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics
No full textThe book illustrates the application of Monte Carlo methods in financial engineering and economics. The book is organized into five parts: introduction and motivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysis and variance reduction; and applications ranging from option pricing and risk management to optimization. Advanced topics like stochastic differential equations, low-discrepancy sequences, stochastic optimization, numerical methods for stochastic dynamic programming, risk measures, and Markov chain Monte Carlo methods are illustrated with practical applications and working R code is provide
From Shortest Paths to Reinforcement Learning: A MATLAB-Based Introduction to Dynamic Programming
No full textDynamic programming (DP) has a relevant history as a powerful and flexible optimization principle, but has a bad reputation as a computationally impractical tool. This book fills a gap between the statement of DP principles and their actual software implementation. Using MATLAB throughout, this tutorial gently gets the reader acquainted with DP and its potential applications, offering the possibility of actual experimentation and hands-on experience. The book assumes basic familiarity with probability and optimization, and is suitable to both practitioners and graduate students in engineering, applied mathematics, management, finance and economics
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