Liquidity-Seeking Execution

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/** Deterministic reference algorithms for D13-F02 Cost/Risk Optimization. */

export type JsonObject = Record<string, unknown>;

function integer(name: string, value: unknown, options: { positive?: boolean; nonnegative?: boolean } = {}): number {
  if (typeof value !== "number" || !Number.isInteger(value)) throw new Error(`${name} must be an integer`);
  if (options.positive && value <= 0) throw new Error(`${name} must be positive`);
  if (options.nonnegative && value < 0) throw new Error(`${name} must be nonnegative`);
  return value;
}

function finiteNumber(name: string, value: unknown, options: { positive?: boolean; nonnegative?: boolean } = {}): number {
  if (typeof value !== "number" || !Number.isFinite(value)) throw new Error(`${name} must be a finite number`);
  if (options.positive && value <= 0) throw new Error(`${name} must be positive`);
  if (options.nonnegative && value < 0) throw new Error(`${name} must be nonnegative`);
  return value;
}

function sideValue(value: unknown): "buy" | "sell" {
  if (value !== "buy" && value !== "sell") throw new Error("side must be 'buy' or 'sell'");
  return value;
}

function validateQuantity(totalQuantity: unknown, lotSize: unknown): [number, number] {
  const total = integer("total_quantity", totalQuantity, { positive: true });
  const lot = integer("lot_size", lotSize, { positive: true });
  if (total % lot !== 0) throw new Error("total_quantity must be divisible by lot_size");
  return [total, lot];
}

function lotFloor(quantity: number, lotSize: number): number {
  return Math.max(0, Math.floor(quantity / lotSize + 1e-12) * lotSize);
}

function round(value: number, digits: number): number {
  const scale = 10 ** digits;
  return Math.round((value + Number.EPSILON) * scale) / scale;
}

function allocateLots(totalQuantity: number, weights: number[], lotSize: number): number[] {
  if (!weights.length || weights.some((value) => !Number.isFinite(value) || value < 0) || weights.reduce((a, b) => a + b, 0) <= 0) {
    throw new Error("allocation weights must be finite, nonnegative, and have positive total");
  }
  const totalLots = totalQuantity / lotSize;
  const weightSum = weights.reduce((a, b) => a + b, 0);
  const exact = weights.map((weight) => totalLots * weight / weightSum);
  const bases = exact.map((value) => Math.floor(value + 1e-12));
  let residual = totalLots - bases.reduce((a, b) => a + b, 0);
  const order = weights.map((_, index) => index).sort((left, right) => {
    const difference = (exact[right] - bases[right]) - (exact[left] - bases[left]);
    return difference !== 0 ? difference : left - right;
  });
  for (const index of order) {
    if (residual <= 0) break;
    bases[index] += 1;
    residual -= 1;
  }
  return bases.map((lots) => lots * lotSize);
}

function signedMoveBps(side: "buy" | "sell", current: number, benchmark: number): number {
  const direction = side === "buy" ? 1 : -1;
  return direction * (current - benchmark) * 10000 / benchmark;
}

export function almgrenChrissOptimalExecution(input: JsonObject): JsonObject {
  const [total, lot] = validateQuantity(input.total_quantity, input.lot_size);
  const intervals = integer("interval_count", input.interval_count, { positive: true });
  const impactWeight = finiteNumber("temporary_impact_weight", input.temporary_impact_weight, { positive: true });
  const riskWeight = finiteNumber("inventory_risk_weight", input.inventory_risk_weight, { nonnegative: true });
  if (total / lot < intervals) throw new Error("interval_count cannot exceed available lots");

  let kappa = 0;
  let rawTrades: number[];
  if (riskWeight === 0) {
    rawTrades = Array(intervals).fill(1);
  } else {
    kappa = Math.acosh(1 + riskWeight / (2 * impactWeight));
    const denominator = Math.sinh(kappa * intervals);
    const holdings = Array.from({ length: intervals + 1 }, (_, step) => total * Math.sinh(kappa * (intervals - step)) / denominator);
    rawTrades = Array.from({ length: intervals }, (_, index) => holdings[index] - holdings[index + 1]);
  }
  const trades = allocateLots(total, rawTrades, lot);
  let remaining = total;
  let impactScore = 0;
  let riskScore = 0;
  const schedule = trades.map((quantity, index) => {
    remaining -= quantity;
    const impactComponent = impactWeight * quantity * quantity;
    const riskComponent = riskWeight * remaining * remaining;
    impactScore += impactComponent;
    riskScore += riskComponent;
    return { interval: index + 1, target_quantity: quantity, target_remaining_quantity: remaining, temporary_impact_score: round(impactComponent, 6), inventory_risk_score: round(riskComponent, 6) };
  });
  return { total_quantity: total, interval_count: intervals, lot_size: lot, temporary_impact_weight: impactWeight, inventory_risk_weight: riskWeight, kappa: round(kappa, 12), scheduled_quantity: trades.reduce((a, b) => a + b, 0), remaining_quantity: remaining, temporary_impact_score: round(impactScore, 6), inventory_risk_score: round(riskScore, 6), objective_score: round(impactScore + riskScore, 6), schedule, state: riskWeight === 0 ? "risk-neutral" : "risk-adjusted" };
}

export function implementationShortfallExecution(input: JsonObject): JsonObject {
  const [remaining, lot] = validateQuantity(input.remaining_quantity, input.lot_size);
  const side = sideValue(input.side);
  const decisionPrice = integer("decision_price_atoms", input.decision_price_atoms, { positive: true });
  const currentPrice = integer("current_price_atoms", input.current_price_atoms, { positive: true });
  const spread = finiteNumber("spread_bps", input.spread_bps, { nonnegative: true });
  const impact = finiteNumber("impact_coefficient_bps", input.impact_coefficient_bps, { nonnegative: true });
  const adv = integer("average_daily_volume", input.average_daily_volume, { positive: true });
  const volatility = finiteNumber("volatility_bps", input.volatility_bps, { nonnegative: true });
  const aversion = finiteNumber("risk_aversion", input.risk_aversion, { nonnegative: true });
  const urgency = finiteNumber("urgency_bps", input.urgency_bps, { nonnegative: true });
  const intervals = integer("intervals_remaining", input.intervals_remaining, { positive: true });
  const maxChild = Math.min(remaining, integer("max_child_quantity", input.max_child_quantity, { positive: true }));
  const candidateStep = integer("candidate_step_quantity", input.candidate_step_quantity, { positive: true });
  if (maxChild % lot !== 0 || candidateStep % lot !== 0) throw new Error("max_child_quantity and candidate_step_quantity must be lot-aligned");
  const signedMove = signedMoveBps(side, currentPrice, decisionPrice);
  const adverseMove = Math.max(0, signedMove);
  const quantities: number[] = [];
  for (let quantity = 0; quantity <= maxChild; quantity += candidateStep) quantities.push(quantity);
  if (quantities[quantities.length - 1] !== maxChild) quantities.push(maxChild);
  const candidates = quantities.map((quantity) => {
    const residual = remaining - quantity;
    const immediate = quantity * (spread / 2 + impact * quantity / adv);
    const opportunity = residual * (adverseMove + urgency / intervals);
    const risk = residual * (aversion * volatility / Math.sqrt(intervals));
    return { child_quantity: quantity, residual_quantity: residual, immediate_cost_score: round(immediate, 6), opportunity_cost_score: round(opportunity, 6), inventory_risk_score: round(risk, 6), total_score: round(immediate + opportunity + risk, 6) };
  });
  const selected = [...candidates].sort((left, right) => left.total_score - right.total_score || left.child_quantity - right.child_quantity)[0];
  return { side, decision_price_atoms: decisionPrice, current_price_atoms: currentPrice, signed_move_bps: round(signedMove, 6), adverse_move_bps: round(adverseMove, 6), remaining_quantity: remaining, selected_child_quantity: selected.child_quantity, post_child_quantity: selected.residual_quantity, selected_total_score: selected.total_score, selected_immediate_cost_score: selected.immediate_cost_score, selected_opportunity_cost_score: selected.opportunity_cost_score, selected_inventory_risk_score: selected.inventory_risk_score, candidates, state: selected.child_quantity > 0 ? "execute-now" : "wait" };
}

export function arrivalPriceExecution(input: JsonObject): JsonObject {
  const [remaining, lot] = validateQuantity(input.remaining_quantity, input.lot_size);
  const side = sideValue(input.side);
  const arrival = integer("arrival_price_atoms", input.arrival_price_atoms, { positive: true });
  const current = integer("current_price_atoms", input.current_price_atoms, { positive: true });
  const tolerance = finiteNumber("tolerance_bps", input.tolerance_bps, { nonnegative: true });
  const marketVolume = integer("observed_market_volume", input.observed_market_volume, { nonnegative: true });
  const baseRate = integer("base_participation_bps", input.base_participation_bps, { nonnegative: true });
  const defensiveRate = integer("defensive_participation_bps", input.defensive_participation_bps, { nonnegative: true });
  const maxRate = integer("max_participation_bps", input.max_participation_bps, { positive: true });
  const intervals = integer("intervals_remaining", input.intervals_remaining, { positive: true });
  const deadline = integer("deadline_threshold_intervals", input.deadline_threshold_intervals, { positive: true });
  const maxChild = integer("max_child_quantity", input.max_child_quantity, { positive: true });
  if (!(0 <= defensiveRate && defensiveRate <= baseRate && baseRate <= maxRate && maxRate <= 10000)) throw new Error("participation rates must satisfy 0 <= defensive <= base <= max <= 10000");
  if (maxChild % lot !== 0) throw new Error("max_child_quantity must be lot-aligned");
  const signedMove = signedMoveBps(side, current, arrival);
  let priceState: string;
  let chosenRate: number;
  if (intervals <= deadline) { priceState = "deadline-override"; chosenRate = maxRate; }
  else if (signedMove <= -tolerance) { priceState = "favorable"; chosenRate = maxRate; }
  else if (signedMove >= tolerance) { priceState = "adverse"; chosenRate = defensiveRate; }
  else { priceState = "inside-band"; chosenRate = baseRate; }
  const target = lotFloor(marketVolume * chosenRate / 10000, lot);
  const child = Math.min(remaining, maxChild, target);
  return { side, arrival_price_atoms: arrival, current_price_atoms: current, signed_move_bps: round(signedMove, 6), tolerance_bps: tolerance, price_state: priceState, chosen_participation_bps: chosenRate, observed_market_volume: marketVolume, target_from_volume_quantity: target, child_quantity: child, remaining_quantity: remaining - child, state: child === remaining ? "parent-complete" : priceState };
}

export function liquiditySeekingExecution(input: JsonObject): JsonObject {
  const [total, lot] = validateQuantity(input.total_quantity, input.lot_size);
  const side = sideValue(input.side);
  const limitPrice = integer("limit_price_atoms", input.limit_price_atoms, { positive: true });
  const minimumConfidence = integer("minimum_confidence_bps", input.minimum_confidence_bps, { nonnegative: true });
  const maxAge = integer("maximum_age_ms", input.maximum_age_ms, { nonnegative: true });
  const maxTake = integer("max_take_per_event", input.max_take_per_event, { positive: true });
  if (minimumConfidence > 10000) throw new Error("minimum_confidence_bps cannot exceed 10000");
  if (maxTake % lot !== 0) throw new Error("max_take_per_event must be lot-aligned");
  if (!Array.isArray(input.liquidity_events) || input.liquidity_events.length === 0) throw new Error("liquidity_events must be a nonempty array");
  let remaining = total;
  let accepted = 0;
  const events = (input.liquidity_events as unknown[]).map((raw, index) => {
    if (raw === null || typeof raw !== "object" || Array.isArray(raw)) throw new Error(`liquidity_events[${index}] must be an object`);
    const event = raw as JsonObject;
    if (typeof event.event_id !== "string" || !event.event_id.trim()) throw new Error(`liquidity_events[${index}].event_id must be a nonempty string`);
    const price = integer(`liquidity_events[${index}].price_atoms`, event.price_atoms, { positive: true });
    const available = integer(`liquidity_events[${index}].available_quantity`, event.available_quantity, { nonnegative: true });
    const age = integer(`liquidity_events[${index}].age_ms`, event.age_ms, { nonnegative: true });
    const confidence = integer(`liquidity_events[${index}].confidence_bps`, event.confidence_bps, { nonnegative: true });
    if (confidence > 10000) throw new Error(`liquidity_events[${index}].confidence_bps cannot exceed 10000`);
    let reason: string;
    let quantity = 0;
    if (remaining === 0) reason = "parent-complete";
    else if (age > maxAge) reason = "stale";
    else if (confidence < minimumConfidence) reason = "confidence-below-threshold";
    else if ((side === "buy" && price > limitPrice) || (side === "sell" && price < limitPrice)) reason = "outside-limit";
    else { quantity = Math.min(remaining, maxTake, lotFloor(available, lot)); reason = quantity > 0 ? "accepted" : "below-one-lot"; }
    remaining -= quantity;
    accepted += quantity;
    return { event_id: event.event_id.trim(), price_atoms: price, available_quantity: available, age_ms: age, confidence_bps: confidence, planned_take_quantity: quantity, reason, remaining_quantity: remaining };
  });
  return { side, limit_price_atoms: limitPrice, total_quantity: total, accepted_quantity: accepted, remaining_quantity: remaining, accepted_event_count: events.filter((row) => row.reason === "accepted").length, rejected_event_count: events.filter((row) => row.reason !== "accepted").length, events, state: remaining === 0 ? "parent-complete" : accepted > 0 ? "opportunity-found" : "no-eligible-liquidity" };
}

export function opportunisticDarkPoolExecution(input: JsonObject): JsonObject {
  const [total, lot] = validateQuantity(input.total_quantity, input.lot_size);
  const maxFraction = integer("maximum_dark_fraction_bps", input.maximum_dark_fraction_bps, { positive: true });
  const minProbability = integer("minimum_firm_probability_bps", input.minimum_firm_probability_bps, { nonnegative: true });
  const minImprovement = integer("minimum_price_improvement_atoms", input.minimum_price_improvement_atoms, { nonnegative: true });
  const minExecution = integer("minimum_execution_quantity", input.minimum_execution_quantity, { positive: true });
  const maxWindow = integer("max_exposure_per_window", input.max_exposure_per_window, { positive: true });
  const fallback = integer("fallback_window", input.fallback_window, { positive: true });
  if (maxFraction > 10000 || minProbability > 10000) throw new Error("basis-point parameters cannot exceed 10000");
  if (minExecution % lot !== 0 || maxWindow % lot !== 0) throw new Error("minimum_execution_quantity and max_exposure_per_window must be lot-aligned");
  if (!Array.isArray(input.dark_opportunities) || input.dark_opportunities.length === 0) throw new Error("dark_opportunities must be a nonempty array");
  const darkCap = lotFloor(total * maxFraction / 10000, lot);
  let exposed = 0;
  const opportunities = (input.dark_opportunities as unknown[]).map((raw, index) => {
    if (raw === null || typeof raw !== "object" || Array.isArray(raw)) throw new Error(`dark_opportunities[${index}] must be an object`);
    const opportunity = raw as JsonObject;
    if (typeof opportunity.opportunity_id !== "string" || !opportunity.opportunity_id.trim()) throw new Error(`dark_opportunities[${index}].opportunity_id must be a nonempty string`);
    const window = integer(`dark_opportunities[${index}].window`, opportunity.window, { positive: true });
    const indicated = integer(`dark_opportunities[${index}].indicated_quantity`, opportunity.indicated_quantity, { nonnegative: true });
    const probability = integer(`dark_opportunities[${index}].firm_probability_bps`, opportunity.firm_probability_bps, { nonnegative: true });
    const improvement = integer(`dark_opportunities[${index}].price_improvement_atoms`, opportunity.price_improvement_atoms, { nonnegative: true });
    if (probability > 10000) throw new Error(`dark_opportunities[${index}].firm_probability_bps cannot exceed 10000`);
    const capRemaining = Math.max(0, darkCap - exposed);
    let reason: string;
    let quantity = 0;
    if (window >= fallback) reason = "fallback-active";
    else if (probability < minProbability) reason = "firm-probability-below-threshold";
    else if (improvement < minImprovement) reason = "price-improvement-below-threshold";
    else if (indicated < minExecution) reason = "minimum-size-not-met";
    else if (capRemaining === 0) reason = "dark-cap-reached";
    else { quantity = Math.min(capRemaining, maxWindow, lotFloor(indicated, lot)); reason = quantity >= minExecution ? "expose-dark" : "minimum-size-not-met"; if (reason !== "expose-dark") quantity = 0; }
    exposed += quantity;
    return { opportunity_id: opportunity.opportunity_id.trim(), window, indicated_quantity: indicated, firm_probability_bps: probability, price_improvement_atoms: improvement, planned_dark_exposure_quantity: quantity, reason, dark_cap_remaining_quantity: Math.max(0, darkCap - exposed) };
  });
  const fallbackQuantity = total - exposed;
  return { total_quantity: total, maximum_dark_fraction_bps: maxFraction, dark_quantity_cap: darkCap, planned_dark_exposure_quantity: exposed, lit_fallback_quantity: fallbackQuantity, dark_opportunity_count: opportunities.length, accepted_dark_window_count: opportunities.filter((row) => row.reason === "expose-dark").length, opportunities, state: fallbackQuantity === 0 ? "dark-plan-complete" : "lit-fallback-required" };
}

export function calculate(topicId: string, input: JsonObject): JsonObject {
  if (input === null || typeof input !== "object" || Array.isArray(input)) throw new Error("inputs must be an object");
  if (topicId === "D13-F02-A01") return almgrenChrissOptimalExecution(input);
  if (topicId === "D13-F02-A02") return implementationShortfallExecution(input);
  if (topicId === "D13-F02-A03") return arrivalPriceExecution(input);
  if (topicId === "D13-F02-A04") return liquiditySeekingExecution(input);
  if (topicId === "D13-F02-A05") return opportunisticDarkPoolExecution(input);
  throw new Error(`unsupported topic_id: ${topicId}`);
}