Demos

Live, in-browser computations backing the papers on this site.

• Mind the gap — the dealer's game
  Enquiries fall from the sky and land at the best competing quote; you hold a bar whose gap is your bid and offer. Three levels, two symmetries: the hard level (moving price) is the medium one (imbalanced flow) in a moving frame, and the medium level is the easy one (balanced flow) after a skew of δ and a slower inventory clock. A regret meter scores you against the policy-iteration optimum.
• The imbalance symmetry
  The imbalanced and balanced market making problems are solved numerically and independently; after the skew shift δ and the carry multiplier M(q), one lands on the other to solver precision. The dots on the line are the theorem.
• Twin dealers — the commutative square, live
  The imbalanced dealer and her balanced twin at cost M(q)c share one inventory path, trade for trade, on two clocks: quotes a constant δ apart with identical widths, the imbalanced clock slower by exactly 2√(q(1−q)), and carry per transition equal. One-sided flow is a skew plus a time change.
• Optimal and sub-optimal market makers
  Three dealers face the same enquiry stream and the same competing quotes: the optimal policy, constant-width linear-skew with no flow term, and no skew at all. The flow term is worth a few percent of profit; ignoring skew entirely is ruinous.
• The term structure of the flow skew
  The finite-horizon behavior of the equivalence, computed by its own exact spectral representation: the mid displacement is zero at maturity and climbs to −δ at the spectral-gap rate; the spread carries a finite-horizon transient; and a dealer who marks her terminal book at the flow-adjusted price has no transient at all.
• Learning faster with the symmetry
  Reinforcement learning and its inverse across cycling flow regimes. One Q-learner pools all experience into a single balanced-frame policy via the δ shift and earns well above a per-regime baseline. The δ shift alone ignores the carry multiplier M(q), so de-tilted quotes help the inverse estimator at small samples and then stall at that second-order bias.

More demonstrations will appear here as the program's papers are written up.