23,984 research outputs found
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Multi-Period Trading via Convex Optimization
We consider a basic model of multi-period trading, which can be used to
evaluate the performance of a trading strategy. We describe a framework for
single-period optimization, where the trades in each period are found by
solving a convex optimization problem that trades off expected return, risk,
transaction cost and holding cost such as the borrowing cost for shorting
assets. We then describe a multi-period version of the trading method, where
optimization is used to plan a sequence of trades, with only the first one
executed, using estimates of future quantities that are unknown when the trades
are chosen. The single-period method traces back to Markowitz; the multi-period
methods trace back to model predictive control. Our contribution is to describe
the single-period and multi-period methods in one simple framework, giving a
clear description of the development and the approximations made. In this paper
we do not address a critical component in a trading algorithm, the predictions
or forecasts of future quantities. The methods we describe in this paper can be
thought of as good ways to exploit predictions, no matter how they are made. We
have also developed a companion open-source software library that implements
many of the ideas and methods described in the paper
Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection
The classical dynamic programming-based optimal stochastic control methods
fail to cope with nonseparable dynamic optimization problems as the principle
of optimality no longer applies in such situations. Among these notorious
nonseparable problems, the dynamic mean-variance portfolio selection
formulation had posted a great challenge to our research community until
recently. A few solution methods, including the embedding scheme, have been
developed in the last decade to solve the dynamic mean-variance portfolio
selection formulation successfully. We propose in this paper a novel mean-field
framework that offers a more efficient modeling tool and a more accurate
solution scheme in tackling directly the issue of nonseparability and deriving
the optimal policies analytically for the multi-period mean-variance-type
portfolio selection problems
A dynamic programming approach to constrained portfolios
This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption
Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure
The discrete-time mean-variance portfolio selection formulation, a
representative of general dynamic mean-risk portfolio selection problems, does
not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated
pre-committed efficient policy may become inefficient when considering the
corresponding truncated problem, thus stimulating investors' irrational
investment behavior. We investigate analytically effects of portfolio
constraints on time consistency of efficiency for convex cone constrained
markets. More specifically, we derive the semi-analytical expressions for the
pre-committed efficient mean-variance policy and the minimum-variance signed
supermartingale measure (VSSM) and reveal their close relationship. Our
analysis shows that the pre-committed discrete-time efficient mean-variance
policy satisfies TCIE if and only if the conditional expectation of VSSM's
density (with respect to the original probability measure) is nonnegative, or
once the conditional expectation becomes negative, it remains at the same
negative value until the terminal time. Our findings indicate that the property
of time consistency in efficiency only depends on the basic market setting,
including portfolio constraints, and this fact motivates us to establish a
general solution framework in constructing TCIE dynamic portfolio selection
problem formulations by introducing suitable portfolio constraints
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