Martin Branda

Charles University in Prague | CUNI · Department of Probability and Mathematical Statistics

We deal with several sources of uncertainty in electricity markets. The independent system operator (ISO) maximizes the social welfare using chance constraints to hedge against discrepancies between the estimated and real electricity demand. We find an explicit solution to the ISO problem and use it to tackle the problem of a producer. In our model...

We deal with data envelopment analysis models with diversification which can identify investment opportunities efficient with respect to several inputs and outputs represented by risk and return measures. Moreover, they enable to project the inefficient investment opportunity to the efficient frontier and suggest how to revise its structure. Howeve...

We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding...

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A com...

We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding...

We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming problem, which is thus still difficult to solve. Therefore, we apply a Scholtes-type regularization method to obtain...

We deal with fixed interval scheduling (FIS) problems on parallel identical machines where the job starting times are given but the finishing times are subject to uncertainty. In the operational problem, we construct a schedule with the highest worst-case probability that it remains feasible, whereas in the tactical problem we are looking for the m...

The Norwegian company EWOS AS produces fish feed for the salmonfarming industry, supplying approximately 300 customers spread along the coast ofNorway. The feed is produced at three factory locations and distributed by a fleetof 10 dedicated vessels. The high seasonality of the demand and the large number ofcustomers make the distribution planning...

Abstract. The Norwegian company EWOS AS produces fish feed for the salmon farming industry, supplying approximately 300 customers spread along the coast of Norway. The feed is produced at three factory locations and distributed by a fleet of 10 dedicated vessels. The high seasonality of the demand and the large number of customers make the distribu...

We deal with operational fixed interval scheduling problem with random delays in job processing times. We formulate two stochastic programming problems. In the first problem with a probabilistic objective, all jobs are processed on available machines and the goal is to obtain a schedule with the highest attainable reliability. The second problem is...

We deal with an investment problem, where the variance of a portfolio is minimized and at the same time the skewness is maximized. Moreover, we impose a chance (probabilistic) constraint on the portfolio return which must be fulfilled with a high probability. This leads to a difficult nonconvex multiobjective stochastic programming problem. Under d...

We deal with chance constrained problems (CCP) with differentiable nonlinear random functions and discrete distribution. We allow nonconvex functions both in the constraints and in the objective. We reformulate the problem as a mixed-integer nonlinear program, and relax the integer variables into continuous ones. We approach the relaxed problem as...

We introduce data envelopment analysis (DEA) models equivalent to efficiency tests with respect to the -th order stochastic dominance (NSD). In particular, we focus on strong and weak variants of convex NSD efficiency and NSD portfolio efficiency. The proposed DEA models are in relation with strong and weak Pareto–Koopmans efficiencies and employ -...

We propose several formulations of the fixed interval scheduling problem under uncertainty, where the risk is represented by random delays in processing times. We employ various stochastic programming and robust coloring problems to deal with the uncertainty. Our main goal is to introduce equivalent deterministic reformulations of the stochastic pr...

We deal with the problem of an investor who is using a mean-risk model for accessing efficiency of investment opportunities. Our investor employs value at risk on several risk levels at the same time which corresponds to the approach called risk shaping. We review several data envelopment analysis (DEA) models which can deal with negative data. We...

We propose new diversification-consistent DEA models suitable for assessing efficiency of investment opportunities available on financial markets. The formulations based on directional distance measures enable to use several risk measures as inputs and return measures as outputs, which can take both positive and negative values. We show that variou...

We focus on rating of non-life insurance contracts. We employ multiplicative models with basic premium levels and specific surcharge coefficients for various levels of selected risk/rating factors. We use generalized linear models (GLM) to describe the probability distribution of total losses for a contract during one year. We show that the traditi...

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 effici...

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 (2012C) and Wang and Ahmed (2008) on the rates of convergence to the problems with a mixed-integer bounded set of feasible solutions and several expected value constraints. M...

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...

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 the author [“Diversification-consistent data envelopment analysis with...

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 se...

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 compl...

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 ine...

If the constraints in an optimization problem are dependent on a random parameter, we would like to ensure that they are fulfilled with a high level of reliability. The most natural way is to employ chance constraints. However, the resulting problem is very hard to solve. We propose an alternative formulation of stochastic programs using penalty fu...

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...

In this article, the authors deal with the efficiency of world stock indices. Basically, they compare three approaches: mean-risk, data envelopment analysis (DEA), and stochastic dominance (SD) efficiency. In the DEA methodology, efficiency is defined as a weighted sum of outputs compared to a weighted sum of inputs when optimal weights are used. I...

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 are solved. The obtained problems with penalties a...

This paper is a contribution to portfolio efficiency testing using DEA-risk models and stochastic dominance (SD) criteria. Basically, we compare several approaches to portfolio efficiency based either on Data Envelopment Analysis (DEA) or stochastic dominance relations. In the DEA methodology, the efficiency score is defined as a weighted sum of ou...

We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosenpenalty-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...

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...

We study the local stability of the mean-risk model with a conditional value at risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied by R. Schultz and S. Tiedemann [Math. Program. 105, No. 2–3 (B), 365–386 (2006; Zbl 1085.90042)]. First, we generalize the qualitative res...

In this paper we aim at output analysis with respect to changes of the probability distribution for problems with probabilistic (chance) constraints. The perturbations are modeled via contamination of the initial probability distribution. Dependence of the set of solutions on the probability distribution rules out the straightforward construction o...

Development of applicable robustness results for stochastic programs with probabilistic constraints is a demanding task. In this paper we follow the relatively simple ideas of output analysis based on the contamination technique and focus on construction of computable global bounds for the optimal value function. Dependence of the set of feasible s...

Since Markowitz published his pioneer work (15), the performance of a portfolio of assets has been measured by its expected return and risk. However, his model had some drawbacks. Transaction costs, indivisible assets and assymmet- rical quantitation of risk were not included into his investment model. We deal with optimal investment problem with i...