Volume 2010
http://edoc.hu-berlin.de/18452/367
Mon, 20 Mar 2023 13:44:53 GMT2023-03-20T13:44:53ZA computational study of a solver system forprocessing two-stage stochastic linearprogramming problems
http://edoc.hu-berlin.de/18452/9068
A computational study of a solver system forprocessing two-stage stochastic linearprogramming problems
Zverovich, Victor; Fábián, Csaba I.; Ellison, Francis; Mitra, Gautam
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
Mon, 29 Nov 2010 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90682010-11-29T00:00:00ZConstruction of Risk-Averse Enhanced Index Funds
http://edoc.hu-berlin.de/18452/9067
Construction of Risk-Averse Enhanced Index Funds
Lejeune, Miguel; Samatli-Pac, Gülay
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a largeprobability, thereby limiting the market risk exposure of the investors and the moral hazard associated with thewage structure of fund managers. The resulting stochastic integer problem is reformulated through the derivationof a deterministic equivalent for the risk constraint and the use of a block decomposition technique. We developan exact outer approximation method based on the relaxation of some binary restrictions and the reformulation ofthe cardinality constraint. The method provides a hierarchical organization of the computations with expandingsets of integer-restricted variables and outperforms the Bonmin and the Cplex 12.1 solvers. The methodcan solve very large (up to 1000 securities) instances, converges fast, scales well, and is general enough to beapplicable to problems with buy-in threshold constraints. Cross-validation tests show that the constructed fundstrack closely and are consistently less risky than the benchmark on the out-of-sample period.
Fri, 19 Nov 2010 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90672010-11-19T00:00:00ZSampling-based decomposition methods for risk-averse multistage programs
http://edoc.hu-berlin.de/18452/9066
Sampling-based decomposition methods for risk-averse multistage programs
Guigues, Vincent; Römisch, Werner
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We define a risk averse nonanticipative feasible policy for multistage stochastic programsand propose a methodology to implement it. The approach is based on dynamic programmingequations written for a risk averse formulation of the problem.This formulation relies on a new class of multiperiod risk functionals called extended polyhedralrisk measures. Dual representations of such risk functionals are given and used to derive conditionsof coherence. In the one-period case, conditions for convexity and consistency with second orderstochastic dominance are also provided. The risk averse dynamic programming equations arespecialized considering convex combinations of one-period extended polyhedral risk measures suchas spectral risk measures.To implement the proposed policy, the approximation of the risk averse recourse functionsfor stochastic linear programs is discussed. In this context, we detail a stochastic dual dynamicprogramming algorithm which converges to the optimal value of the risk averse problem.
Wed, 20 Oct 2010 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90662010-10-20T00:00:00ZOn joint probabilistic constraints with Gaussian coefficient matrix
http://edoc.hu-berlin.de/18452/9065
On joint probabilistic constraints with Gaussian coefficient matrix
Ackooij, W. Van; Henrion, R.; Möller, A.; Zorgati, R.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
The paper deals with joint probabilistic constraints defined by a Gaussiancoefficient matrix. It is shown how to explicitly reduce the computation ofvalues and gradients of the underlying probability function to that of Gaussiandistribution functions. This allows to employ existing efficient algorithms forcalculating this latter class of function in order to solve probabilistically constrainedoptimization problems of the indicated type. Results are illustratedby an example from energy production.
Tue, 19 Oct 2010 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90652010-10-19T00:00:00Z