Daniel Kuhn

Distributionally Robust Joint Chance Constraints with Second-Order Moment Information

  • Daniel Kuhn
  • Berc Rustem
  • Steve Zymler
    • Categories Robust Optimization Tags , ,

    We develop tractable semidefinite programming (SDP) based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove … Read more

    Generalized Decision Rule Approximations for Stochastic Programming via Liftings

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more

    Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules

  • Daniel Kuhn
  • Paula Rocha
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of … Read more

    An Efficient Method to Estimate the Suboptimality of Affine Controllers

  • Paul J. Goulart
  • Daniel Kuhn
  • Michael J. Hadjiyiannis
    • Categories Control Applications, Robust Optimization Tags ,

    We consider robust output feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such … Read more

    Robust Markov Decision Processes

  • Daniel Kuhn
  • Berc Rustem
  • Wolfram Wiesemann
    • Categories Dynamic Programming, Robust Optimization

    Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider … Read more

    Robust Software Partitioning with Multiple Instantiation

  • Daniel Kuhn
  • Wayne Luk
  • Simon Spacey
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and in size. In particular, hardware components offering high speed tend to accommodate only few code segments. … Read more

    Worst-Case Value-at-Risk of Non-Linear Portfolios

  • Daniel Kuhn
  • Berc Rustem
  • Steve Zymler
    • Categories Finance and Economics, Robust Optimization Tags , , , ,

    Portfolio optimization problems involving Value-at-Risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR … Read more

    Primal and dual linear decision rules in stochastic and robust optimization

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Linear stochastic programming provides a flexible toolbox for analyzing real-life decision situations, but it can become computationally cumbersome when recourse decisions are involved. The latter are usually modelled as decision rules, i.e., functions of the uncertain problem data. It has recently been argued that stochastic programs can quite generally be made tractable by restricting the … Read more

    Robust Portfolio Optimization with Derivative Insurance Guarantees

  • Daniel Kuhn
  • Berc Rustem
  • Steve Zymler
    • Categories Finance and Economics, Robust Optimization Tags , , ,

    Robust portfolio optimization finds the worst-case portfolio return given that the asset returns are realized within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns … Read more

    An information-based approximation scheme for stochastic optimization problems in continuous time

  • Daniel Kuhn
    • Categories Infinite Dimensional Optimization, Stochastic Programming Tags , , , ,

    Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vector are inherently difficult to solve. In fact, scenario tree based algorithms are unsuitable for problems with many stages, while dynamic programming type techniques are unsuitable for problems with many state variables. This article proposes a stage aggregation scheme … Read more