Finance and Economics

Formulation and solution strategies for nonparametric nonlinear stochastic programs, with an application in finance

  • Fabian Bastin
  • Philippe L. Toint
  • Cinzia Cirillo
    • Categories Finance and Economics, Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider a class of stochastic programming models where the uncertainty is classically represented using parametric distributions families. The parameters are then usually estimated together with the optimal value of the problem. However, misspecification of the underlying random variables often leads to irrealistic results when little is known about their true distributions. We propose to … Read more

    A difference of convex formulation of value-at-risk constrained optimization

  • R. Hochreiter
  • Georg Ch. Pflug
  • David Wozabal
    • Categories Finance and Economics, Global Optimization, Stochastic Programming Tags , , ,

    In this article, we present a representation of value-at-risk (VaR) as a difference of convex (D.C.) functions in the case where the distribution of the underlying random variable is discrete and has finitely many atoms. The D.C. representation is used to study a financial risk-return portfolio selection problem with a VaR constraint. A branch-and-bound algorithm … Read more

    A Log-Robust Optimization Approach to Portfolio Management

  • Ban Kawas
  • Aurelie Thiele
    • Categories Finance and Economics, Robust Optimization Tags , ,

    In this paper we present a robust optimization approach to portfolio management under uncertainty that (i) builds upon the well-established Lognormal model for stock prices while addressing its limitations, and (ii) incorporates the imperfect knowledge on the true distribution of the continuously compounded rates of return, i.e., the increments of the logarithm of the stock … Read more

    Robust Efficient Frontier Analysis with a Separable Uncertainty Model

  • Stephen Boyd
  • Seung-Jean Kim
    • Categories Convex Optimization, Finance and Economics, Robust Optimization Tags , , , , , , ,

    Mean-variance (MV) analysis is often sensitive to model mis-specification or uncertainty, meaning that the MV efficient portfolios constructed with an estimate of the model parameters (i.e., the expected return vector and covariance of asset returns) can give very poor performance for another set of parameters that is similar and statistically hard to distinguish from the … Read more

    A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance

  • Stephen Boyd
  • Seung-Jean Kim
    • Categories Convex Optimization, Finance and Economics, Robust Optimization Tags , , , ,

    This paper concerns a fractional function of the form $x^Ta/\sqrt{x^TBx}$, where $B$ is positive definite. We consider the game of choosing $x$ from a convex set, to maximize the function, and choosing $(a,B)$ from a convex set, to minimize it. We prove the existence of a saddle point and describe an efficient method, based on … Read more

    Sample Average Approximation of Expected Value Constrained Stochastic Programs

  • Shabbir Ahmed
  • W. Wang
    • Categories Finance and Economics, Stochastic Programming

    We propose a sample average approximation (SAA) method for stochastic programming problems involving an expected value constraint. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). Our contributions include an analysis of the convergence rate and a statistical validation scheme for the proposed SAA method. Computational results using a portfolio … Read more

    Operations Risk Management by Planning Optimally the Qualified Workforce Capacity

  • Emmanuel Fragnière
  • Jacek Gondzio
  • Xi Yang
    • Categories Applications - OR and Management Sciences, Finance and Economics, Stochastic Programming Tags ,

    Operational risks are defined as risks of human origin. Unlike financial risks that can be handled in a financial manner (e.g. insurances, savings, derivatives), the treatment of operational risks calls for a “managerial approach”. Consequently, we propose a new way of dealing with operational risk, which relies on the well known aggregate planning model. To … 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

    An estimation-free, robust conditional value-at-risk portfolio allocation model

  • Carlos Jabbour
  • Javier F. Peña
  • Juan C. Vera
  • Luis F. Zuluaga
    • Categories Finance and Economics, Robust Optimization, Semi-infinite Programming

    We propose a novel optimization model for risk-averse investors to obtain robust solutions for portfolio allocation problems. Unlike related models in the literature, no historical data or statistical estimation techniques are used to compute the parameters of the model. Instead, the parameters are directly obtained from current prices of options on the assets being considered. … Read more

    The Variational Inequality Approach for Solving Spatial Auction Problems with Joint Constraints

  • Igor V. Konnov
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , ,

    We consider a problem of managing a system of spatially distributed markets under capacity and balance constraints and show that solutions of a variational inequality enjoy auction principle properties implicitly. This enables us to develop efficient tools both for derivation of existence and uniqueness results and for creation of solution methods. CitationKazan University, Kazan, March … Read more