Finance and Economics

On the Implementation of Interior Point Decomposition Algorithms for Two-Stage Stochastic Conic

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Finance and Economics, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and \”{Ozevin} \cite{MO04a,MO04b} and Zhao \cite{GZ01}, however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs … Read more

    Pricing a class of exotic options via moments and SDP relaxations

  • Jean-Bernard Lasserre
  • Thomas Prieto-Rumeau
  • Mihail Zervos
    • Categories Finance and Economics, Optimization of Systems modeled by PDEs

    We present a new methodology for the numerical pricing of a class of exotic derivatives such as Asian or barrier options when the underlying asset price dynamics are modelled by a geometric Brownian motion or a number of mean-reverting processes of interest. This methodology identifies derivative prices with infinite-dimensional linear programming problems involving the moments … Read more

    Constructing Risk Measures from Uncertainty Sets

  • Karthik Natarajan
  • Dessislava Pachamanova
  • Melvyn Sim
    • Categories Finance and Economics, Robust Optimization Tags ,

    We propose a unified theory that links uncertainty sets in robust optimization to risk measures in portfolio optimization. We illustrate the correspondence between uncertainty sets and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these measures. We also show that by using properly defined … Read more

    Non-Linear Stochastic Fractional Programming Models of Financial Derivatives

  • Vincent Charles
  • D Dutta
    • Categories Finance and Economics, Stochastic Programming Tags , ,

    Non-Linear Stochastic Fractional programming models provide numerous insights into a wide variety of areas such as in financial derivatives. Portfolio optimization has been one of the important research fields in modern finance. The most important character within this optimization problem is the uncertainty of the future returns on assets. The objective of this study is … Read more

    Sensitivity analysis in convex quadratic optimization: simultaneous perturbation of the objective and right-hand-side vectors

  • Alireza Ghaffari Hadigheh
  • Oleksandr Romanko
  • Tamás Terlaky
    • Categories Finance and Economics, Linear Programming, Quadratic Programming Tags , , , , , ,

    In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval … Read more

    An Optimization Approach to Computing the Implied Volatility of American Options

  • Arun Sen
    • Categories Complementarity and Variational Inequalities, Finance and Economics, Nonlinear Optimization Tags , ,

    We present a method to compute the implied volatility of American options as a mathematical program with equilibrium constraints. The formulation we present is new, as are the convergence results we prove. The algorithm holds the promise of being practical to implement, and we demonstrate some preliminary numerical results to this end. Citation Princeton University … Read more

    Rebalancing an Investment Portfolio in the Presence of Convex Transaction Costs

  • Stephen E. Braun
  • John E. Mitchell
    • Categories Convex Optimization, Finance and Economics, Linear, Cone and Semidefinite Programming Tags ,

    The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which convex transaction costs are incurred to rebalance an investment portfolio. In particular, we consider linear, piecewise linear, and quadratic transaction costs. The Markowitz framework of mean-variance efficiency … Read more

    Robust Profit Opportunities in Risky Financial Portfolios

  • Mustafa C. Pinar
  • Reha H. Tütüncü
    • Categories Finance and Economics, Robust Optimization Tags , ,

    For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single and multiple period settings. We show that the problem of finding the “most robust” profit opportunity can be solved as a convex quadratic programming problem, and investigate its relation to the Sharpe … Read more

    Leader-Follower Equilibria for Electric Power and NO_x Allowances Markets

  • Yihsu Chen
  • Sven Leyffer
  • Todd S. Munson
  • Benjamin Hobbs
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , ,

    This paper investigates the ability of the largest producer in an electricity market to manipulate both the electricity and emission allowances markets to its advantage. A Stackelberg game to analyze this situation is constructed in which the largest firm plays the role of the leader, while the medium-sized firms are treated as Cournot followers with … Read more

    Recovering Risk-Neutral Probability Density Functions from Options Prices using Cubic Splines

  • Ana M. Monteiro
  • Reha H. Tütüncü
  • Luis Nunes Vicente
    • Categories Finance and Economics, Quadratic Programming, Semi-definite Programming Tags , , , ,

    We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and … Read more