risk measures

Guaranteed Bounds for General Non-discrete Multistage Risk-Averse Stochastic Optimization Programs

  • Francesca Maggioni
  • Georg Ch. Pflug
    • Categories Stochastic Programming Tags , , , , ,

    In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such ”infinite” problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e. finite … Read more

    Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

  • Vincent Guigues
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic … Read more

    A Quantitative Comparison of Risk Measures

  • Alois Pichler
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags ,

    The choice of a risk measure reflects a subjective preference of the decision maker in many managerial, or real world economic problem formulations. To evaluate the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We … Read more

    Minimizing Risk Exposure when the Choice of a Risk Measure is Ambiguous

  • Erick Delage
  • Jonathan Yu-Meng Li
    • Categories Applications - OR and Management Sciences Tags , ,

    Since the financial crisis of 2007-2009, there has been a renewed interest toward quantifying more appropriately the risks involved in financial positions. Popular risk measures such as variance and value-at-risk have been found inadequate as we now give more importance to properties such as monotonicity, convexity, translation invariance, scale invariance, and law invariance. Unfortunately, the … Read more

    Machine Learning and Portfolio Optimization

  • Gah-Yi Ban
  • Noureddine El Karoui
  • Andrew E.B. Lim
    • Categories Applications - OR and Management Sciences, Finance and Economics Tags , , , ,

    The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, … Read more

    Multilevel Optimization Modeling for Risk-Averse Stochastic Programming

  • Jonathan Eckstein
  • Jingnan Fan
  • Deniz Eskandani
    • Categories Stochastic Programming Tags , , ,

    Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which uncertainty is resolved at more than one stage, however, using coherent risk measures within a standard single-level optimization framework becomes problematic. To avoid severe time-consistency difficulties, the current state of the art is to … Read more

    Bounds for nested law invariant coherent risk measures

  • Alexander Shapiro
  • Linwei Xin
    • Categories Dynamic Programming, Stochastic Programming Tags , , , ,

    With every law invariant coherent risk measure is associated its conditional analogue. In this paper we discuss lower and upper bounds for the corresponding nested (composite) formulations of law invariant coherent risk measures. In particular, we consider the Average Value-at-Risk and comonotonic risk measures. ArticleDownload View PDF

    Time Consistency Decisions and Temporal Decomposition of Coherent Risk Functionals

  • Georg Ch. Pflug
  • Alois Pichler
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags , ,

    It is well known that most risk measures (risk functionals) are time inconsistent in the following sense: It may happen that today some loss distribution appears to be less risky than another, but looking at the conditional distribution at a later time, the opposite relation holds. In this article we demonstrate that this time inconsistency … Read more

    Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

  • Naomi Miller
  • Andrzej Ruszczyński
    • Categories Stochastic Programming Tags , ,

    We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct two decomposition methods for solving the problem. The first … Read more

    Satisficing measures for analysis of risky positions

  • David B. Brown
  • Melvyn Sim
    • Categories Finance and Economics Tags , , , , , ,

    In this work we introduce a class of measures for evaluating the quality of financial positions based on their ability to achieve desired financial goals. In the spirit of Simon (1959), we call these measures satisficing measures and show that they are dual to classes of risk measures. This approach has the advantage that aspiration … Read more