5,796 research outputs found
Strict Solution Method for Linear Programming Problem with Ellipsoidal Distributions under Fuzziness
This paper considers a linear programming problem with ellipsoidal distributions including fuzziness. Since this problem is not well-defined due to randomness and fuzziness, it is hard to solve it directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed model is transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve the main problem analytically and efficiently due to nonlinear programming, the solution method is constructed introducing an appropriate parameter and performing the equivalent transformations
Portfolio Selection with Two-Stage Preferences
We propose a model of portfolio selection under ambiguity, based on a two-stage valuation procedure which disentangles ambiguity and ambiguity aversion. The model does not imply 'extreme pessimism' from the part of the investor, as multiple priors models do. Furthermore, its analytical tractability allows to study complex problems thus far not analyzed, such as joint uncertainty about means and variances of returns.ambiguity, portfolio selection, parameter uncertainty.
Robust utility maximization in markets with transaction costs
We consider a continuous-time market with proportional transaction costs.
Under appropriate assumptions we prove the existence of optimal strategies for
investors who maximize their worst-case utility over a class of possible
models. We consider utility functions defined either on the positive axis or on
the whole real line
Time--consistent investment under model uncertainty: the robust forward criteria
We combine forward investment performance processes and ambiguity averse
portfolio selection. We introduce the notion of robust forward criteria which
addresses the issues of ambiguity in model specification and in preferences and
investment horizon specification. It describes the evolution of time-consistent
ambiguity averse preferences.
We first focus on establishing dual characterizations of the robust forward
criteria. This offers various advantages as the dual problem amounts to a
search for an infimum whereas the primal problem features a saddle-point. Our
approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We
then study in detail non-volatile criteria. In particular, we solve explicitly
the example of an investor who starts with a logarithmic utility and applies a
quadratic penalty function. The investor builds a dynamical estimate of the
market price of risk and updates her stochastic utility in
accordance with the so-perceived elapsed market opportunities. We show that
this leads to a time-consistent optimal investment policy given by a fractional
Kelly strategy associated with . The leverage is proportional to
the investor's confidence in her estimate
Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations
We consider stochastic programs where the distribution of the uncertain
parameters is only observable through a finite training dataset. Using the
Wasserstein metric, we construct a ball in the space of (multivariate and
non-discrete) probability distributions centered at the uniform distribution on
the training samples, and we seek decisions that perform best in view of the
worst-case distribution within this Wasserstein ball. The state-of-the-art
methods for solving the resulting distributionally robust optimization problems
rely on global optimization techniques, which quickly become computationally
excruciating. In this paper we demonstrate that, under mild assumptions, the
distributionally robust optimization problems over Wasserstein balls can in
fact be reformulated as finite convex programs---in many interesting cases even
as tractable linear programs. Leveraging recent measure concentration results,
we also show that their solutions enjoy powerful finite-sample performance
guarantees. Our theoretical results are exemplified in mean-risk portfolio
optimization as well as uncertainty quantification.Comment: 42 pages, 10 figure
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