Finance and Economics

Regularized Stochastic Dual Dynamic Programming for convex nonlinear optimization problems

  • Vincent Guigues
  • Miguel A. Lejeune
  • Wajdi Tekaya
    • Categories Dynamic Programming, Finance and Economics, Stochastic Programming Tags , , , ,

    We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the Stochastic Dual Dynamic Programming (SDDP) … Read more

    Worst-Case Expected Shortfall with Univariate and Bivariate Marginals

  • Bikramjit Das
  • Karthik Natarajan
  • Anulekha Dhara
    • Categories Finance and Economics Tags , , ,

    Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert information is available in terms of bivariate … Read more

    Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities

  • Giancarlo Bigi
  • Mauro Passacantando
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , ,

    A model for Nash-Cournot oligopolistic markets with concave cost functions and a differentiated commodity is analysed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity … Read more

    Decomposition and Optimization in Constructing Forward Capacity Market Demand Curves

  • Eugene Litvinov
  • Feng Zhao
  • Tongxin Zheng
    • Categories Applications - Science and Engineering, Finance and Economics Tags , , , , , , ,

    This paper presents an economic framework for designing demand curves in Forward Capacity Market (FCM). Capacity demand curves have been recognized as a way to reduce the price volatility inherited from fixed capacity requirements. However, due to the lack of direct demand bidding in FCM, obtaining demand curves that appropriately reflect load’s willingness to pay … Read more

    Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

  • Byung-Geun Choi
  • Ruiwei Jiang
  • Napat Rujeerapaiboon
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

    Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more

    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

    A Non-metric Bilevel Location Problem

  • Claudio Arbib
  • Matteo Tonelli
    • Categories Applications - OR and Management Sciences, Facility Planning and Design, Finance and Economics Tags , ,

    We address a bilevel location problem where a leader first decides which facilities to open and their access prices; then, customers make individual decisions minimizing individual costs. In this note we prove that, when access costs do not fulfill metric properties, the problem is NP-hard even if facilities can be opened at no fixed cost. … Read more

    A Distributed Interior-Point KKT Solver for Multistage Stochastic Optimization

  • Hübner Jens
  • Martin Schmidt
  • Marc C. Steinbach
    • Categories Finance and Economics, Parallel Algorithms, Stochastic Programming Tags , , , ,

    Multistage stochastic optimization leads to NLPs over scenario trees that become extremely large when many time stages or fine discretizations of the probability space are required. Interior-point methods are well suited for these problems if the arising huge, structured KKT systems can be solved efficiently, for instance, with a large scenario tree but a moderate … Read more

    Nash Equilibrium in a Pay-as-bid Electricity Market: Part 1 – Existence and Characterisation

  • Didier Aussel
  • Pascale Bendotti
  • Miroslav Pistek
    • Categories Finance and Economics, Nonsmooth Optimization

    We consider a model of a pay-as-bid electricity market based on a multi-leader-common-follower approach where the producers as leaders are at the upper level and the regulator as a common follower is at the lower level. We fully characterise Nash equilibria for this model by describing necessary and sufficient conditions for their existence as well … Read more

    Nash Equilibrium in a Pay-as-bid Electricity Market: Part 2 – Best Response of a Producer

  • Didier Aussel
  • Pascale Bendotti
  • Miroslav Pistek
    • Categories Finance and Economics, Nonsmooth Optimization

    We consider a multi-leader-common-follower model of a pay-as-bid electricity market in which the producers provide the regulator with either linear or quadratic bids. We prove that for a given producer only linear bids can maximise his profit. Such linear bids are referred as the “best response” of the given producer. They are obtained assuming the … Read more