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What are the best ways to model and analyze rare events in decision-making?

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Decision-making under uncertainty and risk often involves rare events that have significant consequences, such as natural disasters, epidemics, accidents, or cyberattacks. How can you model and analyze these events to make informed choices and mitigate their impacts? In this article, you will learn about some of the best ways to deal with rare events in operations research, such as:

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Abdulrahman Alshanqiti, ACSI, CME4

Equity Analyst | Portfolio Manager | Advisor | Biostatistician | Science/Financial Writer.

1 Probability distributions

One of the most common ways to model rare events is to use probability distributions that capture their frequency and severity. For example, you can use a Poisson distribution to model the number of events that occur in a given time interval, or a Pareto distribution to model the size of events that follow a power law. Probability distributions allow you to calculate the expected value, variance, and other statistics of rare events, as well as perform sensitivity analysis and scenario planning.

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Abdulrahman Alshanqiti, ACSI, CME4

Equity Analyst | Portfolio Manager | Advisor | Biostatistician | Science/Financial Writer.
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As an analyst, I rely on probability distributions to understand rare events. Think of Poisson as a flashlight, illuminating event frequency, and Pareto as a compass for event sizes. They go beyond stats; they offer personal insight into market unpredictability. With them, I calculate expected values, prepare for extraordinary events, and navigate risks. They're tools for "what if" scenarios, making me better equipped for financial journeys.

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2 Monte Carlo simulation

Another way to model and analyze rare events is to use Monte Carlo simulation, which is a technique that generates random samples from a probability distribution or a complex system. By running many simulations, you can estimate the likelihood and outcomes of rare events, as well as their uncertainty and variability. Monte Carlo simulation can also help you compare different alternatives and strategies, and identify the most robust and optimal solutions.

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Abdulrahman Alshanqiti, ACSI, CME4

Equity Analyst | Portfolio Manager | Advisor | Biostatistician | Science/Financial Writer.
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We rely on Monte Carlo simulation for portfolio management and economic forecasting. It's a linchpin in our analytical toolkit, helping us optimize asset allocation, assess risk, and make informed decisions amid economic uncertainties. Monte Carlo's ability to simulate diverse scenarios is invaluable in navigating the intricate world of finance and economic analysis.

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3 Extreme value theory

A more advanced way to model and analyze rare events is to use extreme value theory, which is a branch of statistics that focuses on the behavior of the largest or smallest values in a sample or a population. Extreme value theory can help you estimate the probability and magnitude of extreme events that are beyond the range of historical data or normal distributions, such as the maximum flood level, the minimum temperature, or the worst-case loss. Extreme value theory can also help you model the dependence and correlation between rare events, and their impact on risk measures.

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Abdulrahman Alshanqiti, ACSI, CME4

Equity Analyst | Portfolio Manager | Advisor | Biostatistician | Science/Financial Writer.
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We employ EVT for asset allocation, ensuring our investments are judiciously distributed, considering their susceptibility to tail risks. When it comes to derivative pricing, EVT provides invaluable insights into tail risk, which is essential for precise valuation. But its most critical role is in portfolio management, where EVT's ability to identify and quantify risks from rare, extreme events is a game-changer.

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4 Bayesian inference

Another way to model and analyze rare events is to use Bayesian inference, which is a method that combines prior knowledge and data to update beliefs and estimates. Bayesian inference can help you deal with uncertainty and ambiguity in rare events, as well as incorporate new information and feedback. Bayesian inference can also help you quantify the credibility and confidence of your predictions and decisions, and account for different sources of error and bias.

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5 Agent-based modeling

A final way to model and analyze rare events is to use agent-based modeling, which is a technique that simulates the interactions and behaviors of individual agents in a complex system. Agent-based modeling can help you capture the dynamics and emergence of rare events, as well as their cascading and nonlinear effects. Agent-based modeling can also help you explore the diversity and heterogeneity of agents, and their responses and adaptations to rare events.

Rare events pose significant challenges and opportunities for decision-making under uncertainty and risk. By using these methods, you can model and analyze rare events more effectively and efficiently, and improve your operations research skills and outcomes.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are the best ways to model and analyze rare events in decision-making?

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3

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1 Probability distributions

2 Monte Carlo simulation

3 Extreme value theory

4 Bayesian inference

5 Agent-based modeling

6 Here’s what else to consider

Operations Research

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What are the best ways to model and analyze rare events in decision-making?

1

2

3

4

5

6

1 Probability distributions

2 Monte Carlo simulation

3 Extreme value theory

4 Bayesian inference

5 Agent-based modeling

6 Here’s what else to consider

Operations Research

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