skwdro.operations_research.Portfolio

class skwdro.operations_research.Portfolio(rho=0.01, eta=0.0, alpha=0.95, C=None, d=None, fit_intercept=None, cost='t-NC-1-1', solver='dedicated', solver_reg=0.001, reparam='softmax', n_zeta_samples: int = 10, seed: int = 0, opt_cond: ~skwdro.solvers.optim_cond.OptCondTorch | None = <skwdro.solvers.optim_cond.OptCondTorch object>)[source]

A Wasserstein Distributionally Robust Mean-Risk Portfolio estimator.

Model for the portfolio optimization problem

$\mathbb{E}[ - \langle x ; \xi \rangle ] + \eta \mathrm{CVar}_\alpha[- \langle x ; \xi \rangle]$

which amounts to using the following loss function

$\ell(x,\tau;\xi) = - \langle x ; \xi \rangle + \eta \tau + \frac{1}{\alpha} \max( - \langle x ; \xi \rangle - \tau ; 0)$

where $\tau$ is an extra real parameter accounting for the threshold of the CVaR (see [Rockafellar and Uryasev (2000)]). The parameter $x$ is constrained to live in the simplex (This is encoded in the constraints of the problem in [Esfahani et al. (2018)] and by an exponential reparametrization for the entropy-regularized version).

Parameters:

rhofloat, default=1e-2: Robustness radius
eta: float > 0, default=0: Risk-aversion parameter linked to the Conditional Value at Risk
alpha: float in (0,1], default=0.95: Confidence level of the Conditional Value at Risk
C(nb_constraints, nb_assets), default=None: Matrix of constraints observed by the user.
d(nb_constraints,), default=None: Vector of constraints observed by the user.
fit_intercept: boolean, default=None: Determines if an intercept is fit or not
cost: str, default=”t-NC-1-1”: Tiret-separated code to define the transport cost: “<engine>-<cost id>-<k-norm type>-<power>” for $c(x, y):=\|x-y\|_k^p$
solver: str, default=’entropic’: Solver to be used: ‘entropic’ or ‘dedicated’
solver_reg: float, default=1.0: regularization value for the entropic solver
reparam: str, default=”softmax”: Reparametrization method of theta for the entropic torch loss
random_state: int, default=None: Seed used by the random number generator when using non-deterministic methods on the estimator
Examples
>>> from skwdro.estimators import Portfolio
>>> import numpy as np
>>> X = np.random.normal(size=(10,2))
>>> estimator = Portfolio()
>>> estimator.fit(X)
Portfolio()
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