Martin Branda

Charles University, Prague, Department of probability and mathematical statistics, Post-Doc

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Address: Prague, Hlavni mesto Praha, Czech Republic

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DEA models equivalent to general <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="h...

Operations Research Letters, 2016

Local stability and differentiability of the Conditional Value at Risk defined on the mixed-integer loss functions

Kybernetika -Praha-

format_quoteThe decomposition algorithm addresses continuity of the mean-risk model, enhancing problem-solving in stochastic integer programming with CVaR.format_quote

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Diversification-consistent DEA-risk tests - solution techniques and an empirical comparison

In this paper, we will propose numerically tractable formulations of the diversification-consiste... more In this paper, we will propose numerically tractable formulations of the diversification-consistent DEA tests, which generalize traditional DEA tests as well as mean-risk models. We employ general deviation measures to measure risk of the investment opportunities. We will compare strength of the tests and give characterizations of efficient and inefficient investment opportunities. US industry representative portfolios will be ranked using the proposed DEA tests.

format_quoteStandard DEA tests overlook asset dependencies, leading to misleading assessments of efficient investment opportunities.format_quote

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Optimization Approaches to Multiplicative Tariff of Rates Estimation in Non-Life Insurance

Asia-Pacific Journal of Operational Research, 2014

From Stochastic Dominance to Dea-Risk Models: Portfolio Efficiency Analysis

International Workshop of "Stochastic Programming for Implementation and Advanced Applications", 2012

Exact Penalization in Stochastic Programming—Calmness and Constraint Qualification

Advances in Decision Sciences, 2014

We deal with the conditions which ensure exact penalization in stochastic programming problems un... more We deal with the conditions which ensure exact penalization in stochastic programming problems under finite discrete distributions. We give several sufficient conditions for problem calmness including graph calmness, existence of an error bound, and generalized Mangasarian-Fromowitz constraint qualification. We propose a new version of the theorem on asymptotic equivalence of local minimizers of chance constrained problems and problems with exact penalty objective. We apply the theory to a problem with a stochastic vanishing constraint.

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Mean-value at risk portfolio efficiency: approaches based on data envelopment analysis models with negative data and their empirical behaviour

4OR, 2015

Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

Journal of Optimization Theory and Applications, 2016

Flow-based formulations for operational fixed interval scheduling problems with random delays

by Štěpán Hájek and Martin Branda

Computational Management Science, 2016

Fixed interval scheduling under uncertainty – A tabu search algorithm for an extended robust coloring formulation

Computers & Industrial Engineering, 2016

Solving real-life portfolio problem using stochastic programming and Monte-Carlo techniques

Reformulation of general chance constrained problems using the penalty functions

We explore reformulation of nonlinear stochastic programs with several joint chance constraints b... more We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [5, 9]. The obtained problems with penalties and with a ﬁxed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems using Monte-Carlo simulation techniques for the cases when the set of feasible solution is ﬁnite or inﬁnite bounded. The approach is applied to the ﬁnancial optimization problem with Value at Risk constraint, transaction costs and integer allocations. We compare the ability to generate a feasible solution of the original chance constrained problem using the sample approximations of the chance constraints directly or via sample approximation of the penalty function objective.

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Reformulations of input–output oriented DEA tests with diversification

We deal with diversification-consistent data envelopment analysis (DEA) tests suitable for access... more We deal with diversification-consistent data envelopment analysis (DEA) tests suitable for accessing financial efficiency of investment opportunities. We will show that under nonnegative inputs and outputs, input–output oriented tests with variable return to scale introduced by M. Branda (2013) [7] are equivalent to input oriented tests with nonincreasing return to scale proposed by J.D. Lamb and K.-H. Tee (2012) [14]. Moreover, we will derive a linear programming formulation of the tests with CVaR deviations.

Chance constrained problems: penalty reformulation and performance of sample approximation technique

Sample approximation technique for mixed-integer stochastic programming problems with several chance constraints

The paper deals with sample approximation applied to stochastic programming problems with chance ... more The paper deals with sample approximation applied to stochastic programming problems with chance constraints. We extend results on rates of convergence for problems with mixed-integer bounded sets of feasible solutions and several chance constraints. We derive estimates on the sample size necessary to get a feasible solution of the original problem using sample approximation. We present an application to a vehicle routing problem with time windows, random travel times, and random demand.

On relations between DEA-risk models and stochastic dominance efficiency tests

In this paper, several concepts of portfolio efficiency testing are compared, based either on dat... more In this paper, several concepts of portfolio efficiency testing are compared, based either on data envelopment analysis (DEA) or the second-order stochastic dominance (SSD) relation: constant return to scale DEA models, variable return to scale (VRS) DEA models, diversification-consistent DEA models, pairwise SSD efficiency tests, convex SSD efficiency tests and full SSD portfolio efficiency tests. Especially, the equivalence between VRS DEA model with binary weights and the SSD pairwise efficiency test is proved. DEA models equivalent to convex SSD efficiency tests and full SSD portfolio efficiency tests are also formulated. In the empirical application, the efficiency testing of 48 US representative industry portfolios using all considered DEA models and SSD tests is presented. The obtained efficiency sets are compared. A special attention is paid to the case of small number of the inputs and outputs. It is empirically shown that DEA models equivalent either to the convex SSD test or to the SSD portfolio efficiency test work well even with quite small number of inputs and outputs. However, the reduced VRS DEA model with binary weights is not able to identify all the pairwise SSD efficient portfolios.

On relations between chance constrained and penalty function problems under discrete distributions

We extend the theory of penalty functions to stochastic programming problems with nonlinear inequ... more We extend the theory of penalty functions to stochastic programming problems with nonlinear inequality constraints dependent on a random vector with known distribution. We show that the problems with penalty objective, penalty constraints and chance constraints are asymptotically equivalent under discretely distributed random parts. This is a complementary result to Branda (Kybernetika 48(1):105–122, 2012a), Branda and Dupačová (Ann Oper Res 193(1):3–19, 2012), and Ermoliev et al. (Ann Oper Res 99:207–225, 2000) where the theorems were restricted to continuous distributions only. We propose bounds on optimal values and convergence of optimal solutions. Moreover, we apply exact penalization under modified calmness property to improve the results.

Sample approximation technique for mixed-integer stochastic programming problems with expected value constraints

This paper deals with the theory of sample approximation techniques applied to stochastic program... more This paper deals with the theory of sample approximation techniques applied to stochastic programming problems with expected value constraints. We extend the results of Branda (Optimization 61(8):949–968, 2012c) and Wang and Ahmed (Oper Res Lett 36:515–519, 2008) on the rates of convergence to the problems with a mixed-integer bounded set of feasible solutions and several expected value constraints. Moreover, we enable non-iid sampling and consider Hölder-calmness of the constraints. We derive estimates on the sample size necessary to get a feasible solution or a lower bound on the optimal value of the original problem using the sample approximation. We present an application of the estimates to an investment problem with the Conditional Value at Risk constraints, integer allocations and transaction costs.

Diversification-consistent data envelopment analysis with general deviation measures

We propose new efficiency tests which are based on traditional DEA models and take into account p... more We propose new efficiency tests which are based on traditional DEA models and take into account portfolio diversification. The goal is to identify the investment opportunities that perform well without specifying our attitude to risk. We use general deviation measures as the inputs and return measures as the outputs. We discuss the choice of the set of investment opportunities including portfolios with limited number of assets. We compare the optimal values (efficiency scores) of all proposed tests leading to the relations between the sets of efficient opportunities. Strength of the tests is then discussed. We test the efficiency of 25 world financial indices using new DEA models with CVaR deviation measures.► New DEA efficiency tests which take into account portfolio diversification are proposed. ► General deviation measures are used as the inputs and return measures as the outputs. ► The choice of the set of investment opportunities including portfolios with limited number of assets is discussed. ► The strength of the proposed tests is compared. ► The efficiency of 25 world financial indices is investigated before and during crises.

DEA-Risk Efficiency and Stochastic Dominance Efficiency of Stock Indices

Martin Branda

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