Optimization is at the heart of quantitative finance — from calibrating models to executing trades and managing risk, it powers every decision.
Stay tuned for our upcoming video on must-know optimization techniques used in Quant Finance. Today's question is a classic arbitrage optimization problem solvable using:
-Integer programming (for small n)
-Greedy heuristics (for larger n)
-LP relaxation + rounding
#TeaserTuesdays Problem 41(www.linkedin.com/feed/update/urn:li:activity:73534…)
Q: You’re given n exchanges, all quoting the same stock — but at different prices. Each trade you make incurs a transaction cost.
You’re allowed to do at most one trade per exchange:
Buy (xᵢ = -1)
Sell (xᵢ = +1)
Or do nothing (xᵢ = 0)
But here’s the constraint: you can’t hold a position — the total number of buys must equal the sells.
Goal: Maximize arbitrage profit after transaction costs.
Mathematically:
Maximize ∑ xᵢ * pᵢ − ∑ |xᵢ| * tᵢ
Subject to: ∑ xᵢ = 0 and xᵢ ∈ {−1, 0, 1}
This is a Mixed Integer Optimization Problem.
Example (4 exchanges):
Prices = [99, 101, 102, 98], transaction cost = 1
Buy at D (98 + 1 = 99)
Sell at C (102 − 1 = 101)
Profit = 2
Optimal solution:
x_D = −1, x_C = +1, rest = 0
2 - 0
Thank you @MehulMehta-Quant for inviting me to your podcast and asking the much-needed questions related to Quant Research! https://youtu.be/ASP9CAU_awg?si=C-6Ax... watch video on watch page
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How NOT to solve this Quant Finance interview question! Are you practicing brain teaser questions with us on LinkedIn
#TeaserTuesdays?
Check this one 👇🏼
www.linkedin.com/posts/quantifyyourcareer_teasertu…
1 - 0
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