My first technical post for Macrocosm: using the gradients of an economic simulator to work out which questions the data can answer, before spending anything on calibration. Applied to the Brock-Hommes market model.
Our ICAIF 2025 paper — a generative model that learns fund managers’ strategies from holdings, without specifying a utility function.
Analysing investment strategies through factor models and machine learning, this article examines fund classifications, portfolio stability, and strategy replication. It highlights systematic differences across investment styles and explores how neural networks can model fund manager behaviour.
A workshop paper introducing Evology — an empirically calibrated agent-based model that treats US equity mutual funds as an ecology of competing strategies.
A workshop paper using Evology — a calibrated market-ecology agent-based model — as a training environment to search for trading strategies.
A preprint with Yoshua Bengio and colleagues — using retroactive pricing and prediction markets to correct the Social Cost of Carbon.
Our paper on market ecology is out in PNAS — treating trading strategies as species to explain how markets misprice and destabilise.
Solving the Black-Scholes PDE on a grid. The explicit FTCS scheme and the implicit Crank-Nicolson scheme for a European call, the two spatial grids (S and log S) and the coefficients each requires, conditional stability, boundary conditions, and convergence to the analytical value.
Conservative interior tests for the Mandelbrot set — exact cardioid and period-2 checks plus Monte-Carlo-calibrated period-3 disks — that eliminate ~40% of iteration work with zero false positives.
The Fourier cosine series expansion method for pricing European options. Derives the COS formula from the characteristic function of the log-price process, covers chi and psi payoff coefficients, truncation range selection, and demonstrates convergence under geometric Brownian motion.
Monte Carlo simulation for pricing European, digital and Asian options under Black-Scholes dynamics. Covers convergence properties, antithetic variates, bump-and-revalue sensitivity estimation, and control variates for variance reduction.
Modelling a financial system’s debts as a directed graph and simplifying them. Netting through a clearing party, a trust-constrained reduction algorithm, the fixed-cost variant as Subset Sum, and dependent debt as Minimum Cost Feedback Arc Set, with an NP-hardness reduction from Vertex Cover.
Turning diversification into a graph problem. Building a correlation graph from stock returns, casting a maximally diversified portfolio as Maximum Independent Set / Maximum Clique, and benchmarking exact Bron-Kerbosch enumeration against the Halldórsson-Boppana approximation on the S&P 500.
Testing the efficient market hypothesis by searching foreign-exchange tick data for arbitrage. Currencies become a gain graph, arbitrage becomes a negative cycle, the search is NP-hard, and four methods (exhaustive enumeration, ant colony optimization, Bellman-Ford, and Karp’s minimum mean weight cycle) are benchmarked on 2008 and 2012 tick data.