probabilistic programming

On mixed integer reformulations of monotonic probabilistic programming problems with discrete distributions

  • Vladimir I. Norkin
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , ,

    The paper studies large scale mixed integer reformulation approach to stochastic programming problems containing probability and quantile functions, under assumption of discreteness of the probability distribution involved. Jointly with general sample approximation technique and contemporary mixed integer programming solvers the approach gives a regular framework to solution of practical probabilistic programming problems. In the literature … Read more

    A VaR Black-Litterman Model for the Construction of Absolute Return Fund-of-Funds

  • Miguel A. Lejeune
    • Categories Finance and Economics, Stochastic Programming Tags , , , , , ,

    The objective of this study is to construct fund-of-funds (FoF) that follow an absolute return strategy and meet the requirements imposed by the Value-at-Risk (VaR) market risk measure. We propose the VaR-Black Litterman model which accounts for the VaR and trading (diversification, buy-in threshold, liquidity, currency) requirements. The model takes the form of a probabilistic … Read more

    A Short Note on the Probabilistic Set Covering Problem

  • Anureet Saxena
    • Categories 0-1 Programming, Cutting Plane Approaches, Stochastic Programming Tags , , ,

    In this paper we address the following probabilistic version (PSC) of the set covering problem: min { cx | P (Ax>= xi) >= p, x_{j} in {0,1} j in N} where A is a 0-1 matrix, xi is a random 0-1 vector and p in (0,1] is the threshold probability level. In a recent development … Read more

    MIP Reformulations of the Probabilistic Set Covering Problem

  • Vineet Goyal
  • Miguel A. Lejeune
  • Anureet Saxena
    • Categories 0-1 Programming, Cutting Plane Approaches, Stochastic Programming Tags , , ,

    In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more