The integer constraint problem in finance
Classical Markowitz optimization produces continuous weights — but real portfolios trade in integer lot sizes, have minimum position sizes, and must respect regulatory concentration limits. Relaxing these constraints and rounding produces feasible but suboptimal portfolios. The combinatorial version is NP-hard, and branch-and-bound solvers scale poorly beyond a few hundred assets. NEROX solves these problems as QUBOs in seconds.
Discrete portfolio selection
Select assets subject to cardinality constraints, minimum lot sizes, sector exposure limits, and integer share quantities — constraints that standard quadratic programming ignores.
Index tracking & replication
Construct a sparse portfolio that minimizes tracking error against a benchmark index using fewer assets than the index. Cardinality-constrained tracking error minimization as a QUBO.
Execution scheduling
Break large orders into child orders and schedule execution across trading sessions to minimize market impact while meeting regulatory constraints on pace and venue.
Risk parity rebalancing
Rebalance portfolios at rebalancing dates while minimizing turnover cost. Handles integer lot constraints, transaction costs, and tax efficiency constraints.
Credit portfolio optimization
Select and size credit exposures subject to issuer concentration limits, rating band constraints, and duration targets across a fixed income portfolio.
Regulatory considerations
NEROX runs entirely within your infrastructure on Business and Enterprise plans. No position data, trade sizes, or portfolio holdings are transmitted to Anthropic or any third party. The solver stack is air-gapped deployable for firms with strict data residency requirements.
Getting started
See the Portfolio Optimization problem page for detailed API documentation and code examples including sector constraints and index tracking.