#### Overview of this book

Simulation modeling helps you to create digital prototypes of physical models to analyze how they work and predict their performance in the real world. With this comprehensive guide, you'll understand various computational statistical simulations using Python. Starting with the fundamentals of simulation modeling, you'll understand concepts such as randomness and explore data generating processes, resampling methods, and bootstrapping techniques. You'll then cover key algorithms such as Monte Carlo simulations and Markov decision processes, which are used to develop numerical simulation models, and discover how they can be used to solve real-world problems. As you advance, you'll develop simulation models to help you get accurate results and enhance decision-making processes. Using optimization techniques, you'll learn to modify the performance of a model to improve results and make optimal use of resources. The book will guide you in creating a digital prototype using practical use cases for financial engineering, prototyping project management to improve planning, and simulating physical phenomena using neural networks. By the end of this book, you'll have learned how to construct and deploy simulation models of your own to overcome real-world challenges.
Preface
Section 1: Getting Started with Numerical Simulation
Free Chapter
Chapter 1: Introducing Simulation Models
Chapter 2: Understanding Randomness and Random Numbers
Chapter 3: Probability and Data Generation Processes
Section 2: Simulation Modeling Algorithms and Techniques
Chapter 4: Exploring Monte Carlo Simulations
Chapter 5: Simulation-Based Markov Decision Processes
Chapter 6: Resampling Methods
Chapter 7: Using Simulation to Improve and Optimize Systems
Section 3: Real-World Applications
Chapter 8: Using Simulation Models for Financial Engineering
Chapter 9: Simulating Physical Phenomena Using Neural Networks
Chapter 10: Modeling and Simulation for Project Management
Chapter 11: What's Next?
Other Books You May Enjoy

# Studying risk models for portfolio management

Having a good risk measure is of fundamental importance in finance, as it is one of the main tools for evaluating financial assets. This is because it allows you to monitor securities and provides a criterion for the construction of portfolios. One measure, more than any other, that has been widely used over the years is variance.

## Using variance as a risk measure

The advantage of a diversified portfolio in terms of risk and the expected value allows us to find the right allocation for the securities. Our aim is to obtain the highest expected value at the same risk or to minimize the risk of obtaining the same expected value. To achieve this, it is necessary to trace the concept of risk back to a measurable quantity, which is generally referred to as the variance. Therefore, by maximizing the expected value of the portfolio returns for each level of variance, it is possible to reconstruct a curve called the efficient frontier, which...