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Divide & Ponder

Vague ventures stumbling through computer science

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Private Equity: Risk and Outlook

Private equity (PE) is acquiring ownership of—or a stake in—a company that is not publicly listed on an exchange. A typical PE firm will invest in a portfolio of companies to create a fund open to investors with the promise of future distributed returns. However, unlike shares traded …

Value at Risk and Expected Shortfall

At its core, financial risk management is concerned with quantifying potential losses to assess the downside of financial endeavors and prepare for worst-case scenarios. Perhaps the two most salient risk measures in the field of risk management are value at risk (VaR) and expected shortfall , also known as conditional value …

Jan 2025 Jane Street Puzzle Write-up

This month's puzzle asks us to find a valid solution to a Sudoku grid (shown above) with some special constraints. Here's the puzzle description: Fill the empty cells in the grid above with digits such that each row, column, and outlined 3-by-3 box contains the same set of nine unique digits[1], and such that the nine 9-digit numbers[2] formed by the rows of the grid has the highest-possible GCD…

Surprising Results from Off-center Measurements of Circles

The radius of a circle is defined as the distance from the circle's center to any point on its circumference. If you move the point of measurement to be off-center (as in the figure above), the distances to the circle's circumference are no longer all equal to the circle's radius. But what if you took the mean all of those individual distances—would you recover the value of the radius? In this…

Root-finding Algorithms and Graphical Interpretations

In many quantitative disciplines, problems can often be framed as the task of finding the value — or set of values — that make some expression equal zero. For example, we may want to find the theoretical break-even point of a firm (when profit is equal to zero) or under what conditions a dynamical system is at equilibrium (when the rate of change of the system is zero).