Finance and Economics

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 concave optimization-based approach for sparse portfolio selection

  • David Di Lorenzo
  • Giampaolo Liuzzi
  • Francesco Rinaldi
  • Fabio Schoen
  • Marco Sciandrone
    • Categories Constrained Nonlinear Optimization, Finance and Economics, Stochastic Approaches Tags , , ,

    This paper considers a portfolio selection problem in which portfolios with minimum number of active assets are sought. This problem is motivated by the need of inducing sparsity on the selected portfolio to reduce transaction costs, complexity of portfolio management, and instability of the solution. The resulting problem is a difficult combinatorial problem. We propose … Read more

    Applying a global optimisation algorithm to Fund of Hedge Funds portfolio optimisation

  • Bernard Minsky
  • M Obradovic
  • Qi Tang
  • Rishi Thapar
    • Categories Applications - OR and Management Sciences, Finance and Economics, Global Optimization Tags , , ,

    Portfolio optimisation for a Fund of Hedge Funds (“FoHF”) has to address the asymmetric, non-Gaussian nature of the underlying returns distributions. Furthermore, the objective functions and constraints are not necessarily convex or even smooth. Therefore traditional portfolio optimisation methods such as mean-variance optimisation are not appropriate for such problems and global search optimisation algorithms could … 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

    On the Solution of Complementarity Problems Arising in American Options Pricing

  • Liming Feng
  • V. Linetsky
  • Jose Luis Morales
  • Jorge Nocedal
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Finance and Economics Tags , ,

    In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution … 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

    On the Role of the Norm Constraint in Portfolio Selection

  • Jun-ya Gotoh
  • Akiko Takeda
    • Categories Finance and Economics Tags , , , , , , , ,

    Recently, several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among such are the norm-constrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in the portfolio optimization from several directions. First, it is shown … Read more

    Asset-Liability Management Modelling with Risk Control by Stochastic Dominance

  • Jacek Gondzio
  • Andreas Grothey
  • Xi Yang
    • Categories Finance and Economics, Parallel Algorithms, Stochastic Programming Tags , , ,

    An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to measure … 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

    Short Sales in Log-Robust Portfolio Management

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

    This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral … Read more