IRIS Pol. Torinohttps://iris.polito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Fri, 07 May 2021 22:37:40 GMT2021-05-07T22:37:40Z102031Direct Data-Driven Portfolio Optimization with Guaranteed Shortfall Probabilityhttp://hdl.handle.net/11583/2503507Titolo: Direct Data-Driven Portfolio Optimization with Guaranteed Shortfall Probability
Abstract: This paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: ({\em i}) one needs to make rather strong assumptions on the market for eliciting a return distribution, and ({\em ii}) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimated.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11583/25035072013-01-01T00:00:00ZLagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutionshttp://hdl.handle.net/11583/2619534Titolo: Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions
Abstract: State-of-the-art techniques for simultaneous localization
and mapping (SLAM) employ iterative nonlinear optimization
methods to compute an estimate for robot poses. While
these techniques often work well in practice, they do not provide
guarantees on the quality of the estimate. This paper shows that
Lagrangian duality is a powerful tool to assess the quality of a
given candidate solution. Our contribution is threefold. First, we
discuss a revised formulation of the SLAM inference problem.
We show that this formulation is probabilistically grounded and
has the advantage of leading to an optimization problem with
quadratic objective. The second contribution is the derivation
of the corresponding Lagrangian dual problem. The SLAM
dual problem is a (convex) semidefinite program, which can be
solved reliably and globally by off-the-shelf solvers. The third
contribution is to discuss the relation between the original SLAM
problem and its dual. We show that from the dual problem,
one can evaluate the quality (i.e., the suboptimality gap) of a
candidate SLAM solution, and ultimately provide a certificate
of optimality. Moreover, when the duality gap is zero, one can
compute a guaranteed optimal SLAM solution from the dual
problem, circumventing non-convex optimization. We present
extensive (real and simulated) experiments supporting our claims
and discuss practical relevance and open problems
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11583/26195342015-01-01T00:00:00ZSparse identification of posynomial modelshttp://hdl.handle.net/11583/2619525Titolo: Sparse identification of posynomial models
Abstract: Posynomials are nonnegative combinations of monomials with possibly fractional and both positive and negative exponents. Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural design, mainly due to the fact that design problems cast in terms of posynomial objectives and constraints can be solved efficiently by means of a convex optimization technique known as geometric programming (GP). However, while quite a vast literature exists on GP-based design, very few contributions can yet be found on the problem of identifying posynomial models from experimental data. Posynomial identification amounts to determining not only the coefficients of the combination, but also the exponents in the monomials, which renders the identification problem hard. In this paper, we propose an approach to the identification of multivariate posynomial models based on the expansion on a given large-scale basis of monomials. The model is then identified by seeking coefficients of the combination that minimize a mixed objective, composed by a term representing the fitting error and a term inducing sparsity in the representation, which results in a problem formulation of the “square-root LASSO” type, with nonnegativity constraints on the variables. We propose to solve the problem via a sequential coordinate-minimization scheme, which is suitable for large-scale implementations. A numerical example is finally presented, dealing with the identification of a posynomial model for a NACA 4412 airfoil.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11583/26195252015-01-01T00:00:00ZAn Affine Control Method for Optimal DynamicAsset Allocation with Transaction Costshttp://hdl.handle.net/11583/2284910Titolo: An Affine Control Method for Optimal DynamicAsset Allocation with Transaction Costs
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11583/22849102009-01-01T00:00:00ZA Linear Reaction Technique for Dynamic Asset Allocation in the Presence of Transaction Costshttp://hdl.handle.net/11583/1894280Titolo: A Linear Reaction Technique for Dynamic Asset Allocation in the Presence of Transaction Costs
Abstract: Institutional investors manage their strategic mix of asset classes over time to achieve favorable returns in spite of uncertainties. A fundamental issue in this context is to maintain risk under control while achieving the desired return targets. When the asset mix is to be re-balanced many times over the investment horizon, the decision maker faces a rather difficult constrained dynamic optimization problem that should take into account conditional decisions based on future market behavior. This problem is usually solved approximately using scenario-based stochastic programming: a technique that suffers from serious problems of numerical complexity due to the intrinsic combinatorial nature of scenario trees. In this paper, we present a novel and computationally efficient approach to constrained discrete-time dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon, and may account for proportional transaction costs and intertemporal dependence of the return process. A key feature of the proposed method is the introduction of a linearly-parameterized class of feedback reaction functions, which permits to obtain explicit analytic expressions for the portfolio statistics over time. These expressions are proved to be convex in the decision parameters, hence the multi-stage problem is formulated and solved by means of efficient tools for quadratic or second-order-cone convex programming.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11583/18942802008-01-01T00:00:00ZA flow optimization approach for the rebalancing of mobility on demand systemshttp://hdl.handle.net/11583/2689964Titolo: A flow optimization approach for the rebalancing of mobility on demand systems
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/26899642017-01-01T00:00:00ZA Network Model for an Urban Bike Sharing Systemhttp://hdl.handle.net/11583/2689960Titolo: A Network Model for an Urban Bike Sharing System
Abstract: In this paper, we study and implement a model of the “ToBike” bike sharing
system, located in the city of Turin, Italy. The system is modeled through a closed queuing
network. A thorough data analysis phase is executed on the logged dataset provided by the
service provider, to assess the stationarity properties of the system and to estimate the system
parameters. In particular, customer arrival rates, not directly available, are estimated from
station throughput measurements through a sparse optimization technique. The parameters are
then used to perform predictions of the system behavior over an unseen validation dataset.
While the accuracy provided by asymptotic methods, like mean value analysis, is quite limited,
numerical simulations of the closed queueing network offer viable predictions, especially when
realistic patterns for the customer behavior are considered.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/26899602017-01-01T00:00:00ZCutting plane methods for probabilistically-robust feasibility problemshttp://hdl.handle.net/11583/1409011Titolo: Cutting plane methods for probabilistically-robust feasibility problems
Abstract: Many robust control problems can be formulated in abstract form as convex feasibility programs where one seeks a solution vector x that satisfies a set of inequalities of the form F={f(x,delta) <= 0}. This set typically contains an infinite and uncountable number of inequalities, and it has been proved that the related robust feasibility problem is numerically hard to solve in general. In this paper, we discuss a family of cutting plane methods that solve efficiently a probabilistically-relaxed version of the problem. Specifically, under suitable hypotheses, we show that a cutting plane scheme based on a probabilistic oracle returns in a finite and pre-specified number of iterations a solution which is feasible for most of the members of F, except possibly for a subset having arbitrarily small probability measure.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11583/14090112006-01-01T00:00:00ZPolynomial-Time Random Generation of Uniform Real Matrices in the Spectral Norm Ballhttp://hdl.handle.net/11583/1408965Titolo: Polynomial-Time Random Generation of Uniform Real Matrices in the Spectral Norm Ball
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11583/14089652000-01-01T00:00:00ZA Set-Valued Non-Linear Filter for Robust Localizationhttp://hdl.handle.net/11583/1408963Titolo: A Set-Valued Non-Linear Filter for Robust Localization
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/11583/14089632001-01-01T00:00:00Z