TL;DR

An optimization technique that breaks a complex problem into overlapping subproblems, solving each once and storing the result. It requires optimal substructure and overlapping subproblems.

By Valenke Exam Prep Team·Last updated 2026-06-03

Dynamic Programming

An optimization technique that breaks a complex problem into overlapping subproblems, solving each once and storing the result. It requires optimal substructure and overlapping subproblems.

Why it matters for interviews

DP solves optimal stopping, American option pricing, optimal execution, and many interview brain teasers. The ability to formulate a problem as a DP recursion and solve it efficiently is a highly valued quant skill.

Definition and Mathematical Foundation

An optimization technique that breaks a complex problem into overlapping subproblems, solving each once and storing the result. It requires optimal substructure and overlapping subproblems.

Application in Quantitative Finance

Related Concepts

Backward Induction

Related Terms

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Frequently Asked Questions

What is the Bellman equation?▼

The fundamental recursion of DP: \( V(s) = \max_a [r(s,a) + \gamma V(s')] \). The value of state s is the maximum over actions of immediate reward plus discounted future value. It is the continuous analog of backward induction.

How is DP used for optimal execution?▼

Almgren-Chriss optimal execution: minimize expected cost plus risk penalty of trading a large order over a fixed horizon. The state is remaining inventory; the control is the trading rate. DP yields the optimal schedule.

What is the difference between top-down and bottom-up DP?▼

Top-down (memoization): recurse from the full problem, cache results. Bottom-up (tabulation): fill a table from base cases forward. Both have the same complexity; bottom-up avoids recursion overhead.