StochasticEdge - Monte Carlo + Analytical Engine

This project is a C++ toolkit that solves classic quant-trading interview puzzles using two distinct methods:

1. Monte Carlo simulation: Numerically estimating the optimal strategy and expected value by simulating millions of trials.
2. Closed-form analytical derivation: Deriving the exact answer mathematically and verifying it matches the simulation.

The project features an extensible, low-latency C++17 Monte Carlo engine capable of running millions of trials in milliseconds.

Puzzle Modules

Puzzle Name	Category	One-Line Takeaway
Kelly Criterion	Bankroll Management	Over-betting positive EV games increases variance and guarantees ruin.
Gambler's Ruin	Probability / Markov	Hitting a distant target before ruin scales unfavorably against small edges.
St. Petersburg Paradox	EV / Utility Theory	Infinite EV is meaningless if tails are too fat; you must use log utility.
Expected Value Auction	Game Theory	In a first-price auction, optimal bidding requires shading your bid below your true valuation.
Secretary Problem	Optimal Stopping	Skip the first 37% (1/e) to maximize your chances of picking the absolute best.
Guess 2/3 Average	Iterated Game Theory	Rational players iteratively scaling down expectations converge to 0 (Nash Equilibrium).
Bayesian Updating	Probability / Stats	Every noisy signal pulls your posterior mean toward the signal, weighted by relative precision.
Card Counting EV	Conditional Prob	True count linearly shifts the EV by altering the composition of remaining cards.
Iterated Prisoner's Dilemma	Repeated Games	Tit-For-Tat dominates random strategies by enforcing cooperation and punishing defection.
Market-Making Spread	Market Microstructure	Optimal spread perfectly balances capturing noise trader spread vs. adverse selection from informed flow.

Build and Run

To compile and run the puzzles (Requires C++14 or newer):

mkdir build && cd build
cmake ..
cmake --build .

# Run a specific puzzle
.\puzzle_solver.exe market_making_spread 1000000

(Alternatively, you can compile directly via g++ -std=c++14 -Iinclude src/main.cpp -o puzzle_solver)

To generate convergence plots, run the python script (requires pandas and matplotlib):

python scripts/plot_convergence.py