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', learning_rate: float | None = None, n_zeta_samples: int = 10, random_state: int = 0, n_iter: int | ~typing.Tuple[int, int] | None=None, opt_cond: OptCondTorch | None = <skwdro.solvers.optim_cond.OptCondTorch object>)

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

learning_rate: float | None, default=None

if not set, use a default value depending on the problem, else specifies the stepsize of the gradient descent algorithm

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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