The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Andrzej Ruszczynski - One of the best experts on this subject based on the ideXlab platform.
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optimization problems with second order stochastic dominance constraints Duality compact formulations and cut generation methods
Siam Journal on Optimization, 2008Co-Authors: Gabor Rudolf, Andrzej RuszczynskiAbstract:For stochastic optimization problems with second order stochastic dominance constraints we develop a new form of the Duality Theory featuring measures on the product of the probability space and the real line. We present two formulations involving small numbers of variables and exponentially many constraints: primal and dual. The dual formulation reveals connections between dominance constraints, generalized transportation problems, and the Theory of measures with given marginals. Both formulations lead to two classes of cutting plane methods. Finite convergence of both methods is proved in the case of finitely many events. Numerical results for a portfolio problem are provided.
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portfolio optimization with stochastic dominance constraints
Journal of Banking and Finance, 2006Co-Authors: Darinka Dentcheva, Andrzej RuszczynskiAbstract:We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and Duality Theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.
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portfolio optimization with stochastic dominance constraints
Journal of Banking and Finance, 2006Co-Authors: Darinka Dentcheva, Andrzej RuszczynskiAbstract:Abstract We consider the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return rate. We develop optimality and Duality Theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.
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optimality and Duality Theory for stochastic optimization problems with nonlinear dominance constraints
Mathematical Programming, 2004Co-Authors: Darinka Dentcheva, Andrzej RuszczynskiAbstract:We consider a new class of optimization problems involving stochastic dominance constraints of second order. We develop a new splitting approach to these models, optimality conditions and Duality Theory. These results are used to construct special decomposition methods.
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optimization of convex risk functions
Risk and Insurance, 2004Co-Authors: Andrzej Ruszczynski, Alexander ShapiroAbstract:We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization Theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and Duality Theory for problems involving risk functions.
Erhan Bayraktar - One of the best experts on this subject based on the ideXlab platform.
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optimal investment with random endowments and transaction costs Duality Theory and shadow prices
Mathematics and Financial Economics, 2019Co-Authors: Erhan BayraktarAbstract:This paper studies the utility maximization problem on the terminal wealth with both random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system (CPS) such that the liquidation value processes stay above some stochastic thresholds. In the market consisting of one riskless bond and one risky asset, we obtain a type of the super-hedging result. Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the convex Duality analysis. As an important application of the Duality Theory, we provide some sufficient conditions for the existence of a shadow price process with random endowments in a generalized form as well as in the usual sense using acceptable portfolios.
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optimal investment with random endowments and transaction costs Duality Theory and shadow prices
arXiv: Mathematical Finance, 2015Co-Authors: Erhan BayraktarAbstract:This paper studies the utility maximization on the terminal wealth with random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system (CPS) such that the liquidation value processes stay above some stochastic thresholds. In the market consisting of one riskless bond and one risky asset, we obtain a type of super-hedging result. Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the Duality approach. As an important application of the Duality theorem, we provide some sufficient conditions for the existence of a shadow price process with random endowments in a generalized form as well as in the usual sense using acceptable portfolios.
Walter Schachermayer - One of the best experts on this subject based on the ideXlab platform.
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Duality Theory for portfolio optimisation under transaction costs
Annals of Applied Probability, 2016Co-Authors: Christoph Czichowsky, Walter SchachermayerAbstract:We consider the problem of portfolio optimisation with general c adl ag price processes in the presence of proportional transaction costs. In this context, we develop a general Duality Theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is dened by means of a \sandwiched" process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form. MSC 2010 Subject Classication: 91G10, 93E20, 60G48
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Duality Theory for portfolio optimisation under transaction costs
LSE Research Online Documents on Economics, 2014Co-Authors: Christoph Czichowsky, Walter SchachermayerAbstract:We consider the problem of portfolio optimisation with general cadlag price processes in the presence of proportional transaction costs. In this context, we develop a general Duality Theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is defined by means of a "sandwiched" process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form.
Alberto Ravagnani - One of the best experts on this subject based on the ideXlab platform.
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rank metric codes and their Duality Theory
Designs Codes and Cryptography, 2016Co-Authors: Alberto RavagnaniAbstract:We compare the two Duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes. The identities which we derive are very easy to handle, and allow us to re-establish in a very concise way the main results of the Theory of rank-metric codes first proved by Delsarte employing association schemes and regular semilattices. We also show that our identities imply as a corollary the original MacWilliams identities established by Delsarte. We describe how the minimum and maximum rank of a rank-metric code relate to the minimum and maximum rank of the dual code, giving some bounds and characterizing the codes attaining them. Then we study optimal anticodes in the rank metric, describing them in terms of optimal codes (namely, MRD codes). In particular, we prove that the dual of an optimal anticode is an optimal anticode. Finally, as an application of our results to a classical problem in enumerative combinatorics, we derive both a recursive and an explicit formula for the number of $$k \times m$$k×m matrices over a finite field with given rank and $$h$$h-trace.
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rank metric codes and their Duality Theory
arXiv: Information Theory, 2014Co-Authors: Alberto RavagnaniAbstract:We compare the two Duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes. The identities which we derive are very easy to handle, and allow us to re-establish in a very concise way the main results of the Theory of rank-metric codes first proved by Delsarte employing the Theory of association schemes and regular semilattices. We also show that our identities imply as a corollary the original MacWilliams identities established by Delsarte. We describe how the minimum and maximum rank of a rank-metric code relate to the minimum and maximum rank of the dual code, giving some bounds and characterizing the codes attaining them. Then we study optimal anticodes in the rank metric, describing them in terms of optimal codes (namely, MRD codes). In particular, we prove that the dual of an optimal anticode is an optimal anticode. Finally, as an application of our results to a classical problem in enumerative combinatorics, we derive both a recursive and an explicit formula for the number of $k \times m$ matrices over a finite field with given rank and $h$-trace.
Christoph Czichowsky - One of the best experts on this subject based on the ideXlab platform.
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Duality Theory for portfolio optimisation under transaction costs
Annals of Applied Probability, 2016Co-Authors: Christoph Czichowsky, Walter SchachermayerAbstract:We consider the problem of portfolio optimisation with general c adl ag price processes in the presence of proportional transaction costs. In this context, we develop a general Duality Theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is dened by means of a \sandwiched" process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form. MSC 2010 Subject Classication: 91G10, 93E20, 60G48
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Duality Theory for portfolio optimisation under transaction costs
LSE Research Online Documents on Economics, 2014Co-Authors: Christoph Czichowsky, Walter SchachermayerAbstract:We consider the problem of portfolio optimisation with general cadlag price processes in the presence of proportional transaction costs. In this context, we develop a general Duality Theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is defined by means of a "sandwiched" process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form.
