Kartik Krishnan Sivaramakrishnan

A CVaR Scenario-based Framework: Minimizing Downside Risk of Multi-asset Class Portfolios

  • Kartik Krishnan Sivaramakrishnan
  • Robert Stamicar
    • Categories Applications - OR and Management Sciences, Finance and Economics, Stochastic Programming Tags , ,

    Multi-asset class (MAC) portfolios can be comprised of investments in equities, fixed-income, commodities, foreign-exchange, credit, derivatives, and alternatives such as real-estate and private equity. The return for such {\em non-linear} portfolios is {\em asymmetric} with significant tail risk. The traditional Markowitz Mean-Variance Optimization (MVO) framework, that linearizes all the assets in the portfolio and uses … Read more

    Multi-period portfolio optimization with alpha decay

  • Vishv Jeet
  • Kartik Krishnan Sivaramakrishnan
  • Dieter Vandenbussche
    • Categories Finance and Economics Tags , ,

    The traditional Markowitz MVO approach is based on a single-period model. Single period models do not utilize any data or decisions beyond the rebalancing time horizon with the result that their policies are {\em myopic} in nature. For long-term investors, multi-period optimization offers the opportunity to make {\em wait-and-see} policy decisions by including approximate forecasts … Read more

    Properties of a Cutting Plane Method for Semidefinite Programming

  • John E. Mitchell
  • Kartik Krishnan Sivaramakrishnan
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We analyze the properties of an interior point cutting plane algorithm that is based on a semi-infinite linear formulation of the dual semidefinite program. The cutting plane algorithm approximately solves a linear relaxation of the dual semidefinite program in every iteration and relies on a separation oracle that returns linear cutting planes. We show that … Read more

    Lower bounds for approximate factorizations via semidefinite programming

  • Erich Kaltofen
  • Kartik Krishnan Sivaramakrishnan
  • Bin Li
  • Zhengfeng Yang
  • Lihong Zhi
    • Categories Semi-definite Programming Tags , ,

    The problem of approximately factoring a real or complex multivariate polynomial $f$ seeks minimal perturbations $\Delta f$ to the coefficients of the input polynomial $f$ so that the deformed polynomial $f + \Delta f$ has the desired factorization properties. Efficient algorithms exist that compute the nearest real or complex polynomials that has non-trivial factors. (see … Read more

    Properties of a Cutting Plane Method for Semidefinite Programming

  • John E. Mitchell
  • Kartik Krishnan Sivaramakrishnan
    • Categories Linear, Cone and Semidefinite Programming, Nonsmooth Optimization Tags , , , ,

    We analyze the properties of an interior point cutting plane algorithm that is based on a semi-infinite linear formulation of the dual semidefinite program. The cutting plane algorithm approximately solves a linear relaxation of the dual semidefinite program in every iteration and relies on a separation oracle that returns linear cutting planes. We show that … Read more

    A PARALLEL interior point decomposition algorithm for block-angular semidefinite programs

  • Kartik Krishnan Sivaramakrishnan
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , ,

    We present a two phase interior point decomposition framework for solving semidefinite (SDP) relaxations of sparse maxcut, stable set, and box constrained quadratic programs. In phase 1, we suitably modify the {\em matrix completion} scheme of Fukuda et al. \cite{fukuda_et_al} to preprocess an existing SDP into an equivalent SDP in the block-angular form. In phase … Read more

    A conic interior point decomposition approach for large scale semidefinite programming

  • Gema Plaza
  • Kartik Krishnan Sivaramakrishnan
  • Tamás Terlaky
    • Categories Nonsmooth Optimization, Semi-definite Programming Tags , , ,

    We describe a conic interior point decomposition approach for solving a large scale semidefinite programs (SDP) whose primal feasible set is bounded. The idea is to solve such an SDP using existing primal-dual interior point methods, in an iterative fashion between a {\em master problem} and a {\em subproblem}. In our case, the master problem … Read more