12,900 research outputs found
Twenty years of linear programming based portfolio optimization
a b s t r a c t Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features
RM-CVaR: Regularized Multiple -CVaR Portfolio
The problem of finding the optimal portfolio for investors is called the
portfolio optimization problem. Such problem mainly concerns the expectation
and variability of return (i.e., mean and variance). Although the variance
would be the most fundamental risk measure to be minimized, it has several
drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure
that addresses some of the shortcomings of well-known variance-related risk
measures, and because of its computational efficiencies, it has gained
popularity. CVaR is defined as the expected value of the loss that occurs
beyond a certain probability level (). However, portfolio optimization
problems that use CVaR as a risk measure are formulated with a single
and may output significantly different portfolios depending on how the
is selected. We confirm even small changes in can result in huge
changes in the whole portfolio structure. In order to improve this problem, we
propose RM-CVaR: Regularized Multiple -CVaR Portfolio. We perform
experiments on well-known benchmarks to evaluate the proposed portfolio.
Compared with various portfolios, RM-CVaR demonstrates a superior performance
of having both higher risk-adjusted returns and lower maximum drawdown.Comment: accepted by the IJCAI-PRICAI 2020 Special Track AI in FinTec
ASlib: A Benchmark Library for Algorithm Selection
The task of algorithm selection involves choosing an algorithm from a set of
algorithms on a per-instance basis in order to exploit the varying performance
of algorithms over a set of instances. The algorithm selection problem is
attracting increasing attention from researchers and practitioners in AI. Years
of fruitful applications in a number of domains have resulted in a large amount
of data, but the community lacks a standard format or repository for this data.
This situation makes it difficult to share and compare different approaches
effectively, as is done in other, more established fields. It also
unnecessarily hinders new researchers who want to work in this area. To address
this problem, we introduce a standardized format for representing algorithm
selection scenarios and a repository that contains a growing number of data
sets from the literature. Our format has been designed to be able to express a
wide variety of different scenarios. Demonstrating the breadth and power of our
platform, we describe a set of example experiments that build and evaluate
algorithm selection models through a common interface. The results display the
potential of algorithm selection to achieve significant performance
improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa
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A review of portfolio planning: Models and systems
In this chapter, we first provide an overview of a number of portfolio planning models
which have been proposed and investigated over the last forty years. We revisit the
mean-variance (M-V) model of Markowitz and the construction of the risk-return
efficient frontier. A piecewise linear approximation of the problem through a
reformulation involving diagonalisation of the quadratic form into a variable
separable function is also considered. A few other models, such as, the Mean
Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the
Minimax (MM) model which use alternative metrics for risk are also introduced,
compared and contrasted. Recently asymmetric measures of risk have gained in
importance; we consider a generic representation and a number of alternative
symmetric and asymmetric measures of risk which find use in the evaluation of
portfolios. There are a number of modelling and computational considerations which
have been introduced into practical portfolio planning problems. These include: (a)
buy-in thresholds for assets, (b) restriction on the number of assets (cardinality
constraints), (c) transaction roundlot restrictions. Practical portfolio models may also
include (d) dedication of cashflow streams, and, (e) immunization which involves
duration matching and convexity constraints. The modelling issues in respect of these
features are discussed. Many of these features lead to discrete restrictions involving
zero-one and general integer variables which make the resulting model a quadratic
mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the
algorithms and solution methods for this class of problems are also discussed. The
issues of preparing the analytic data (financial datamarts) for this family of portfolio
planning problems are examined. We finally present computational results which
provide some indication of the state-of-the-art in the solution of portfolio optimisation
problems
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
LINEAR PROGRAMMING APPLIED TO FINANCE - BUILDING A GREAT PORTFOLIO INVESTMENT
The stock market has grown steadily in recent years, and several indices have also been created in this market, like IGC, ISE and IBOVESPA. Thinking about this market growth, this paper aims to build an optimal portfolio using linear programming, based on companies simultaneously present in the indices: IGC and ISE. The constraints of the problem will be based on indicators of IBOVESPA. The model will be created to meet the restrictions set and to maximize the portfolio return, always comparing with the return of IBOVESPA, with a time horizon from 2007 until 2012. As results, the developed model was capable to provide better returns in fourteen of the twenty two periods under consideration. Besides, the average return considering all the periods was 0,03404 for the proposed model and -0,02086 for the IBOVESPA portfolio
"Integrating Optimization and Strategic Conservation to Achieve Higher Efficiencies in Land Protection"
Strategic land conservation seeks to select the highest quality lands given limited financial resources. Traditionally conservation officials implement strategic conservation by creating prioritization maps that attempt to identify the lands of highest ecological value or public value from a resource perspective. This paper describes the history of using optimization in strategic conservation and demonstrates how the combination of these approaches can significantly strengthen conservation efforts by making these programs more efficient with public monies.Mathematical Programming, Conservation Optimization, Cost Effectiveness Analysis, Strategic Conservation
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