Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are not known in advance, but can only be forecast or estimated. Several methodologies have therefore been proposed to handle the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem of making estimates of the un...

The paper considers robust optimization to cope with uncertainty about the stock return process in one period option hedging problems. The robust approach relates portfolio choice to uncertainty, making more cautious hedges when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlying stocks and show that for this set the robust problem is a second ...

In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level ...

This paper deals with the problem of probability estimation in the context of coarse data. Probabilities are estimated using the maximum likelihood principle. Our approach presupposes that each imprecise observation underlies a precise one, and that the uncertainty that pervades its observation is epistemic, rather than representing noise. As a consequence, the likelihood function of the illobs...

This paper presents a comprehensive methodology that combines uncertainty quantification, propagation and robustness-based design optimization using a Bayesian framework. Two types of epistemic uncertainty regarding model inputs/parameters are emphasized: (1) uncertainty modeled as p-box, and (2) uncertainty modeled as interval data. A Bayesian approach is used to calibrate the uncertainty mode...

in this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. the first order reliability method (form) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. the sensitivity level ...

1. Abstract This paper presents a design optimization methodology under three sources of uncertainty: physical variability (aleatory); data uncertainty (epistemic) due to sparse or imprecise data; and model uncertainty (epistemic) due to modeling errors/approximations. A likelihood-based method is use to fuse multiple formats of information, and a non-parametric probability density function (PD...

In the context of structural design, risk optimization allows one to find a proper point of balance between the concurrent goals of economy and safety. Risk optimization involves the minimization of total expected costs, which include expected costs of failure. Expected costs of failure are evaluated from nominal failure probabilities, which reflect the analyst’s degree of belief in the structu...

optimization of maintenance resources to maximize the system availability is a major concern in different manufacturing systems. therefore, a lot of effort is put to construct optimization models to reach the maximum availability level and to reduce the costs of lack of availability. however, despite these efforts, data uncertainty in the real world problems was neglected in proposed models whi...