The Expected Hitting Time Approach To Optimal Price Adjustment Problems
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The Expected Hitting Time Approach to Optimal Price Adjustment Problems
We offer a novel approach for solving optimal price adjustment problems, when the underlying process is a Geometric Brownian Motion (GBM) process. Our approach relies on characterizing the cumulative cost of deviation and the cost of adjusting price until the hitting time of the lower or upper barriers. Using this approach, we are able to derive an analytical expression for the cost function, that does not require solving a PDE or running Monte-Carlo simulations. We apply our framework to the real world problem of adjusting domestic energy prices in countries that adopt administratively-set energy price rules. Our toolbox code in Matlab can be easily modified to be used to calculate optimal policies in a wide range of topics in finance, operations management, economics, and natural resource management.
The Oxford Handbook of Pricing Management
Author: Özalp Özer
language: en
Publisher: Oxford University Press (UK)
Release Date: 2012-06-07
A definitive reference to the theory and practice of pricing across industries, environments, and methodologies. It covers all major areas of pricing including, pricing fundamentals, pricing tactics, and pricing management.
Stochastic Calculus and Brownian Motion
"Stochastic Calculus and Brownian Motion" is a comprehensive guide crafted for students and professionals in mathematical sciences, focusing on stochastic processes and their real-world applications in finance, physics, and engineering. We explore key concepts and mathematical foundations of random movements and their practical implications. At its core, the book delves into Brownian motion, the random movement of particles suspended in a fluid, as described by Robert Brown in the 19th century. This phenomenon forms a cornerstone of modern probability theory and serves as a model for randomness in physical systems and financial models describing stock market behaviors. We also cover martingales, mathematical sequences where future values depend on present values, akin to a fair game in gambling. The book demonstrates how martingales are used to model stochastic processes and their calibration in real-world scenarios. Stochastic calculus extends these ideas into continuous time, integrating calculus with random processes. Our guide provides the tools to understand and apply Itô calculus, crucial for advanced financial models like pricing derivatives and managing risks. Written clearly and systematically, the book includes examples and exercises to reinforce concepts and showcase their real-world applications. It serves as an invaluable resource for students, educators, and professionals globally.