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liquidation.py
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liquidation.py
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import numpy as np
import cvxpy as cp
# Problem data
global_indices = list(range(5))
local_indices = [
[0, 1, 2, 3, 4],
[0, 1],
[2, 3],
[3, 4],
[3, 4]
]
reserves = list(map(np.array, [
[4, 4, 4, 4, 4],
[10, 1],
[1, 5],
[40, 50],
[10, 10]
]))
fees = [
.998,
.997,
.997,
.997,
.999
]
current_assets = [
2,
1,
3,
5,
10
]
# Build local-global matrices
n = len(global_indices)
m = len(local_indices)
A = []
for l in local_indices:
n_i = len(l)
A_i = np.zeros((n, n_i))
for i, idx in enumerate(l):
A_i[idx, i] = 1
A.append(A_i)
# Build variables
deltas = [cp.Variable(len(l), nonneg=True) for l in local_indices]
lambdas = [cp.Variable(len(l), nonneg=True) for l in local_indices]
psi = cp.sum([A_i @ (L - D) for A_i, D, L in zip(A, deltas, lambdas)])
# Objective is to liquidate everything into token 4
obj = cp.Maximize(psi[4])
# Reserves after trade
new_reserves = [R + gamma_i*D - L for R, gamma_i, D, L in zip(reserves, fees, deltas, lambdas)]
# Trading function constraints
cons = [
# Balancer pool with weights 5, 4, 3, 2, 1
cp.geo_mean(new_reserves[0], p=np.array([5, 4, 3, 2, 1])) >= cp.geo_mean(reserves[0]),
# Uniswap v2 pools
cp.geo_mean(new_reserves[1]) >= cp.geo_mean(reserves[1]),
cp.geo_mean(new_reserves[2]) >= cp.geo_mean(reserves[2]),
cp.geo_mean(new_reserves[3]) >= cp.geo_mean(reserves[3]),
# Constant sum pool
cp.sum(new_reserves[4]) >= cp.sum(reserves[4]),
new_reserves[4] >= 0,
# Liquidate all assets, except 4
psi[0] + current_assets[0] == 0,
psi[1] + current_assets[1] == 0,
psi[2] + current_assets[2] == 0,
psi[3] + current_assets[3] == 0
]
# Set up and solve problem
prob = cp.Problem(obj, cons)
prob.solve()
print(f"Total liquidated value: {psi.value[4]}")