SAA method based on modified Newton method for stochastic variational inequality with second-order cone constraints and application in portfolio optimization

Shuang Chen (), Li-Ping Pang, Xue-Fei Ma and Dan Li
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Shuang Chen: Information and Engineering College of Dalian University
Li-Ping Pang: Dalian University of Technology
Xue-Fei Ma: Syracuse University
Dan Li: Information and Engineering College of Dalian University

Mathematical Methods of Operations Research, 2016, vol. 84, issue 1, No 6, 129-154

Abstract: Abstract In this paper we apply modified Newton method based on sample average approximation (SAA) to solve stochastic variational inequality with stochastic second-order cone constraints (SSOCCVI). Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one at exponential rate as sample size increases. We apply the theoretical results for solving a class of stochastic second order cone complementarity problems and stochastic programming problems with stochastic second order cone constraints. Some illustrative examples are given to show how the globally convergent method works and the comparison results between our method and other methods. Furthermore, we apply this method to portfolio optimization with loss risk constraints problems.

Keywords: Stochastic variational inequality problem; Stochastic programming; Conic programming; Portfolio optimization (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00186-016-0537-1

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