Sample Scenario Distribution of a Given Set of Input Parameters

This R Shiny web application is designed to compute the minimum monthly savings required to reach a desired final amount of savings after a specified number of years. The app allows users to choose from different distributions for sampling monthly returns: Normal Distribution, Portfolio Distribution, and Empirical Distribution. Users can also upload their own empirical data for sampling returns.

• Input initial amount, desired final amount, number of years, and probability of success.
• Choose the distribution for sampling monthly returns:
  • Normal Distribution
  • Portfolio Distribution
  • Empirical Distribution (with file upload)
• Simulate monthly returns and calculate the required monthly savings.
• Visualize the results with histograms and cumulative distribution functions (CDF).
• Generate insightful textual output based on the calculations.

The underlying mathematical optimization problem aims to determine the minimum monthly savings $S$ that need to be invested to reach the final amount $A_{final}$ with a given probability of success $P_{success}$. It solved by the bisection algorithm.

$$ \min S \quad \text{such that} \quad \Pr\left( A_{\text{end}} \geq A_{\text{final}} \right) \geq P_{\text{success}} $$

• Initial amount $A_{initial}$
• Desired final amount $A_{final}$
• Number of years $N$
• Probability of success $P_{success}$
• Monthly return distribution $R_{monthly}$