def solve(x0, risk_alphas, loadings, srisk, cost_per_trade=DEFAULT_COST, max_risk=0.01): N = len(x0) # don't hold no risk data (likely dead) lim = np.where(srisk.isnull(), 0.0, 1.0) loadings = loadings.fillna(0) srisk = srisk.fillna(0) risk_alphas = risk_alphas.fillna(0) with Model() as m: w = m.variable(N, Domain.inRange(-lim, lim)) longs = m.variable(N, Domain.greaterThan(0)) shorts = m.variable(N, Domain.greaterThan(0)) gross = m.variable(N, Domain.greaterThan(0)) m.constraint( "leverage_consistent", Expr.sub(gross, Expr.add(longs, shorts)), Domain.equalsTo(0), ) m.constraint("net_consistent", Expr.sub(w, Expr.sub(longs, shorts)), Domain.equalsTo(0.0)) m.constraint("leverage_long", Expr.sum(longs), Domain.lessThan(1.0)) m.constraint("leverage_short", Expr.sum(shorts), Domain.lessThan(1.0)) buys = m.variable(N, Domain.greaterThan(0)) sells = m.variable(N, Domain.greaterThan(0)) gross_trade = Expr.add(buys, sells) net_trade = Expr.sub(buys, sells) total_gross_trade = Expr.sum(gross_trade) m.constraint( "net_trade", Expr.sub(w, net_trade), Domain.equalsTo(np.asarray(x0)), # cannot handle series ) # add risk constraint vol = m.variable(1, Domain.lessThan(max_risk)) stacked = Expr.vstack(vol.asExpr(), Expr.mulElm(w, srisk.values)) stacked = Expr.vstack(stacked, Expr.mul(loadings.values.T, w)) m.constraint("vol-cons", stacked, Domain.inQCone()) alphas = risk_alphas.dot(np.vstack([loadings.T, np.diag(srisk)])) gain = Expr.dot(alphas, net_trade) loss = Expr.mul(cost_per_trade, total_gross_trade) m.objective(ObjectiveSense.Maximize, Expr.sub(gain, loss)) m.solve() result = pd.Series(w.level(), srisk.index) return result
def __Update_Z_Constr(pure_model: Model, constr_z: Dict[int, int]) -> Model: Z = pure_model.getVariable('Z') if len(constr_z) == 1: for key, value in constr_z.items(): # only one iteration pure_model.constraint('BB', Z.index(key), Domain.equalsTo(value)) if len(constr_z) >= 2: expression = Expr.vstack([Z.index(key) for key in constr_z.keys()]) values = [value for key, value in constr_z.items()] pure_model.constraint('BB', expression, Domain.equalsTo(values)) return pure_model
def Update_Z_Constr(self): self.Remove_Z_Constr() Z = self.model.getVariable('Z') if len(self.constr) == 1: for key, value in self.constr.items(): # only one iteration self.model.constraint('BB', Z.index(key), Domain.equalsTo(value)) if len(self.constr) >= 2: expression = Expr.vstack( [Z.index(key) for key in self.constr.keys()]) values = [value for key, value in self.constr.items()] self.model.constraint('BB', expression, Domain.equalsTo(values))
def __rotated_quad_cone(model, expr1, expr2, expr3): model.constraint(Expr.vstack(expr1, expr2, expr3), Domain.inRotatedQCone())
def __quad_cone(model, expr1, expr2): model.constraint(Expr.vstack(expr1, expr2), Domain.inQCone())
def Build_Co_Model(self): r = len(self.roads) mu, sigma = self.mu, self.sigma m, n, r = self.m, self.n, len(self.roads) f, h = self.f, self.h M, N = m + n + r, 2 * m + 2 * n + r A = self.__Construct_A_Matrix() A_Mat = Matrix.dense(A) b = self.__Construct_b_vector() # ---- build Mosek Model COModel = Model() # -- Decision Variable Z = COModel.variable('Z', m, Domain.inRange(0.0, 1.0)) I = COModel.variable('I', m, Domain.greaterThan(0.0)) Alpha = COModel.variable('Alpha', M, Domain.unbounded()) # M by 1 vector Beta = COModel.variable('Beta', M, Domain.unbounded()) # M by 1 vector Theta = COModel.variable('Theta', N, Domain.unbounded()) # N by 1 vector # M1_matrix related decision variables ''' [tau, xi^T, phi^T M1 = xi, eta, psi^t phi, psi, w ] ''' # no-need speedup variables Psi = COModel.variable('Psi', [N, n], Domain.unbounded()) Xi = COModel.variable('Xi', n, Domain.unbounded()) # n by 1 vector Phi = COModel.variable('Phi', N, Domain.unbounded()) # N by 1 vector # has the potential to speedup Tau, Eta, W = self.__Declare_SpeedUp_Vars(COModel) # M2 matrix decision variables ''' [a, b^T, c^T M2 = b, e, d^t c, d, f ] ''' a_M2 = COModel.variable('a_M2', 1, Domain.greaterThan(0.0)) b_M2 = COModel.variable('b_M2', n, Domain.greaterThan(0.0)) c_M2 = COModel.variable('c_M2', N, Domain.greaterThan(0.0)) e_M2 = COModel.variable('e_M2', [n, n], Domain.greaterThan(0.0)) d_M2 = COModel.variable('d_M2', [N, n], Domain.greaterThan(0.0)) f_M2 = COModel.variable('f_M2', [N, N], Domain.greaterThan(0.0)) # -- Objective Function obj_1 = Expr.dot(f, Z) obj_2 = Expr.dot(h, I) obj_3 = Expr.dot(b, Alpha) obj_4 = Expr.dot(b, Beta) obj_5 = Expr.dot([1], Expr.add(Tau, a_M2)) obj_6 = Expr.dot([2 * mean for mean in mu], Expr.add(Xi, b_M2)) obj_7 = Expr.dot(sigma, Expr.add(Eta, e_M2)) COModel.objective( ObjectiveSense.Minimize, Expr.add([obj_1, obj_2, obj_3, obj_4, obj_5, obj_6, obj_7])) # Constraint 1 _expr = Expr.sub(Expr.mul(A_Mat.transpose(), Alpha), Theta) _expr = Expr.sub(_expr, Expr.mul(2, Expr.add(Phi, c_M2))) _expr_rhs = Expr.vstack(Expr.constTerm([0.0] * n), Expr.mul(-1, I), Expr.constTerm([0.0] * M)) COModel.constraint('constr1', Expr.sub(_expr, _expr_rhs), Domain.equalsTo(0.0)) del _expr, _expr_rhs # Constraint 2 _first_term = Expr.add([ Expr.mul(Beta.index(row), np.outer(A[row], A[row]).tolist()) for row in range(M) ]) _second_term = Expr.add([ Expr.mul(Theta.index(k), Matrix.sparse(N, N, [k], [k], [1])) for k in range(N) ]) _third_term = Expr.add(W, f_M2) _expr = Expr.sub(Expr.add(_first_term, _second_term), _third_term) COModel.constraint('constr2', _expr, Domain.equalsTo(0.0)) del _expr, _first_term, _second_term, _third_term # Constraint 3 _expr = Expr.mul(-2, Expr.add(Psi, d_M2)) _expr_rhs = Matrix.sparse([[Matrix.eye(n)], [Matrix.sparse(N - n, n)]]) COModel.constraint('constr3', Expr.sub(_expr, _expr_rhs), Domain.equalsTo(0)) del _expr, _expr_rhs # Constraint 4: I <= M*Z COModel.constraint('constr4', Expr.sub(Expr.mul(20000.0, Z), I), Domain.greaterThan(0.0)) # Constraint 5: M1 is SDP COModel.constraint( 'constr5', Expr.vstack(Expr.hstack(Tau, Xi.transpose(), Phi.transpose()), Expr.hstack(Xi, Eta, Psi.transpose()), Expr.hstack(Phi, Psi, W)), Domain.inPSDCone(1 + n + N)) return COModel