331 research outputs found
OSQP: An Operator Splitting Solver for Quadratic Programs
We present a general-purpose solver for convex quadratic programs based on
the alternating direction method of multipliers, employing a novel operator
splitting technique that requires the solution of a quasi-definite linear
system with the same coefficient matrix at almost every iteration. Our
algorithm is very robust, placing no requirements on the problem data such as
positive definiteness of the objective function or linear independence of the
constraint functions. It can be configured to be division-free once an initial
matrix factorization is carried out, making it suitable for real-time
applications in embedded systems. In addition, our technique is the first
operator splitting method for quadratic programs able to reliably detect primal
and dual infeasible problems from the algorithm iterates. The method also
supports factorization caching and warm starting, making it particularly
efficient when solving parametrized problems arising in finance, control, and
machine learning. Our open-source C implementation OSQP has a small footprint,
is library-free, and has been extensively tested on many problem instances from
a wide variety of application areas. It is typically ten times faster than
competing interior-point methods, and sometimes much more when factorization
caching or warm start is used. OSQP has already shown a large impact with tens
of thousands of users both in academia and in large corporations
Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure
Scenario generation is the construction of a discrete random vector to
represent parameters of uncertain values in a stochastic program. Most
approaches to scenario generation are distribution-driven, that is, they
attempt to construct a random vector which captures well in a probabilistic
sense the uncertainty. On the other hand, a problem-driven approach may be able
to exploit the structure of a problem to provide a more concise representation
of the uncertainty.
In this paper we propose an analytic approach to problem-driven scenario
generation. This approach applies to stochastic programs where a tail risk
measure, such as conditional value-at-risk, is applied to a loss function.
Since tail risk measures only depend on the upper tail of a distribution,
standard methods of scenario generation, which typically spread their scenarios
evenly across the support of the random vector, struggle to adequately
represent tail risk. Our scenario generation approach works by targeting the
construction of scenarios in areas of the distribution corresponding to the
tails of the loss distributions. We provide conditions under which our approach
is consistent with sampling, and as proof-of-concept demonstrate how our
approach could be applied to two classes of problem, namely network design and
portfolio selection. Numerical tests on the portfolio selection problem
demonstrate that our approach yields better and more stable solutions compared
to standard Monte Carlo sampling
Applications of biased randomised algorithms and simheuristics to asset and liability management
Asset and Liability Management (ALM) has captured the attention of academics and financial researchers over the last few decades. On the one hand, we need to try to maximise our wealth by taking advantage of the financial market and, on the other hand, we need to cover our payments (liabilities) over time. The purpose of ALM is to give investors a series of resources or techniques to select the appropriate assets on the financial market that respond to the aforementioned two key factors: cover our liabilities and maximise our wealth. This thesis presents a set of techniques that are capable of tackling realistic financial problems without the usual requirement of considerable computational resources. These techniques are based on heuristics and simulation. Specifically, a biased randomised metaheuristic model is developed that has a direct application in the way insurance companies usually operate. The algorithm makes it possible to efficiently select the smallest number of assets, mainly fixed income, on the balance sheet while guaranteeing the company's obligations. This development allows for the incorporating of the credit quality of the issuer of the assets used. Likewise, a portfolio optimisation model with liabilities is developed and solved with a genetic algorithm. The portfolio optimisation problem differs from the usual one in that it is multi-period, and incorporates liabilities over time. Additionally, the possibility of external financing is included when the entity does not have sufficient cash. These conditions give rise to a complex problem that is efficiently solved by an evolutionary algorithm. In both cases, the algorithms are improved with the incorporation of Monte Carlo simulation. This allows the solutions to be robust when considering realistic market situations. The results are very promising. This research shows that simheuristics is an ideal method for this type of problem.La gestión de activos y pasivos (asset and liability management, ALM) ha acaparado la atención de académicos e investigadores financieros en las últimas décadas. Por un lado, debemos tratar de maximizar nuestra riqueza aprovechando el mercado financiero, y por otro, debemos cubrir nuestros pagos (pasivos) a lo largo del tiempo. El objetivo del ALM es dotar al inversor de una serie de recursos o técnicas para seleccionar los activos del mercado financiero adecuados para obedecer a los dos factores clave mencionados: cumplir con nuestros pasivos y maximizar nuestra riqueza. Esta tesis presenta un conjunto de técnicas que son capaces de abordar problemas financieros realistas sin la necesidad habitual de considerables recursos computacionales. Estas técnicas se basan en la heurÃstica y la simulación. En concreto, se desarrolla un modelo metaheurÃstico sesgado que tiene una aplicación directa en la operación habitual de inmunización de las compañÃas de seguros. El algoritmo permite seleccionar eficientemente el menor número de activos, principalmente de renta fija, en el balance y garantizar las obligaciones de la compañÃa. Este desarrollo permite incorporar la calidad crediticia del emisor de los activos utilizados. Asimismo, se desarrolla un modelo de optimización de la cartera con el pasivo y se resuelve con un algoritmo genético. El problema de optimización de la cartera difiere del habitual en que es multiperiodo e incorpora los pasivos a lo largo del tiempo. Además, se incluye la posibilidad de financiación externa cuando la entidad no tiene suficiente efectivo. Estas condiciones dan lugar a un problema complejo que se resuelve eficientemente mediante un algoritmo evolutivo. En ambos casos, los algoritmos se mejoran con la incorporación de la simulación de Montecarlo. Esto permite que las soluciones sean robustas cuando consideramos situaciones de mercado realistas. Los resultados son muy prometedores. Esta investigación demuestra que la simheurÃstica es un método ideal para este tipo de problemas.La gestió d'actius i passius (asset and liability management, ALM) ha acaparat l'atenció d'acadèmics i investigadors financers les darreres dècades. D'una banda, hem de mirar de maximitzar la nostra riquesa aprofitant el mercat financer, i de l'altra, hem de cobrir els nostres pagaments (passius) al llarg del temps. L'objectiu de l'ALM és dotar l'inversor d'una sèrie de recursos o tècniques per seleccionar els actius del mercat financer adequats per obeir als dos factors clau esmentats: complir els passius i maximitzar la nostra riquesa. Aquesta tesi presenta un conjunt de tècniques que són capaces d'abordar problemes financers realistes sense la necessitat habitual de recursos computacionals considerables. Aquestes tècniques es basen en l'heurÃstica i la simulació. En concret, es desenvolupa un model metaheurÃstic esbiaixat que té una aplicació directa a l'operació habitual d'immunització de les companyies d'assegurances. L'algorisme permet seleccionar eficientment el menor nombre d'actius, principalment de renda fixa, al balanç i garantir les obligacions de la companyia. Aquest desenvolupament permet incorporar la qualitat creditÃcia de l'emissor dels actius utilitzats. Aixà mateix, es desenvolupa un model d'optimització de la cartera amb el passiu i es resol amb un algorisme genètic. El problema d'optimització de la cartera difereix de l'habitual en el fet que és multiperÃode i incorpora els passius al llarg del temps. A més, s'inclou la possibilitat de finançament extern quan l'entitat no té prou efectiu. Aquestes condicions donen lloc a un problema complex que es resol eficientment mitjançant un algorisme evolutiu. En tots dos casos, els algorismes es milloren amb la incorporació de la simulació de Montecarlo. Això permet que les solucions siguin robustes quan considerem situacions de mercat realistes. Els resultats són molt prometedors. Aquesta recerca demostra que la simheurÃstica és un mètode ideal per a aquesta mena de problemes.TecnologÃas de la información y de rede
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Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
A Stochastic Programming Approach for Multi-Period Portfolio Optimization
presented in this paper. The basic model involves Multi-Period decisions (portfolio optimization) and deals with the usual uncertainty of investment returns and future liabilities. Therefore, is it well suited to a stochastic programming approach. We consider the problem of rebalancing policy to accomplish some investment’s criteria. Transaction costs have also been a subject of concern in this paper. In particular, a large amount of transactions usually make asset price move in an unfavorable direction. Therefore, the first problem neglects transactions cost while the second does not
05031 Abstracts Collection -- Algorithms for Optimization with Incomplete Information
From 16.01.05 to 21.01.05, the Dagstuhl Seminar 05031 ``Algorithms for Optimization with Incomplete Information\u27\u27 was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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
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