Convergence analysis of stationary points in sample average approximation of stochastic programs with second order stochastic dominance constraints

2013 ◽  
Vol 143 (1-2) ◽  
pp. 31-59 ◽  
Author(s):  
Hailin Sun ◽  
Huifu Xu
Keyword(s):  
Convergence Analysis ◽  
Stochastic Dominance ◽  
Sample Average Approximation ◽  
Second Order ◽  
Stationary Points ◽  
Stochastic Programs ◽  
Order Stochastic Dominance ◽  
Sample Average ◽  
Second Order Stochastic Dominance ◽  
Average Approximation

CONVERGENCE ANALYSIS OF A REGULARIZED SAMPLE AVERAGE APPROXIMATION METHOD FOR STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

2011 ◽  
Vol 28 (06) ◽  
pp. 755-771 ◽  
Author(s):  
YONGCHAO LIU ◽  
GUI-HUA LIN
Keyword(s):  
Convergence Analysis ◽  
Approximation Method ◽  
Regularization Parameter ◽  
Sample Average Approximation ◽  
Stationary Points ◽  
Complementarity Constraints ◽  
One Stage ◽  
Mathematical Programs ◽  
Sample Average ◽  
Average Approximation

Regularization method proposed by Scholtes (2011) has been a recognized approach for deterministic mathematical programs with complementarity constraints (MPCC). Meng and Xu (2006) applied the approach coupled with Monte Carlo techniques to solve a class of one stage stochastic MPCC and presented some promising numerical results. However, Meng and Xu have not presented any convergence analysis of the regularized sample approximation method. In this paper, we fill out this gap. Specifically, we consider a general class of one stage stochastic mathematical programs with complementarity constraint where the objective and constraint functions are expected values of random functions. We carry out extensive convergence analysis of the regularized sample average approximation problems including the convergence of statistical estimators of optimal solutions, C-stationary points, M-stationary points and B-stationary points as sample size increases and the regularization parameter tends to zero.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

scholarly journals Sample average approximation of stochastic dominance constrained programs

2010 ◽  
Vol 133 (1-2) ◽  
pp. 171-201 ◽  
Author(s):  
Jian Hu ◽  
Tito Homem-de-Mello ◽  
Sanjay Mehrotra
Keyword(s):  
Stochastic Dominance ◽  
Sample Average Approximation ◽  
Sample Average ◽  
Average Approximation

scholarly journals Whale Optimization Algorithm for Multiconstraint Second-Order Stochastic Dominance Portfolio Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Q. H. Zhai ◽  
T. Ye ◽  
M. X. Huang ◽  
S. L. Feng ◽  
H. Li
Keyword(s):  
Portfolio Optimization ◽  
Optimization Algorithm ◽  
Stochastic Dominance ◽  
Optimization Model ◽  
Second Order ◽  
Whale Optimization Algorithm ◽  
Order Stochastic Dominance ◽  
Whale Optimization ◽  
Portfolio Optimization Model ◽  
Second Order Stochastic Dominance

In the field of asset allocation, how to balance the returns of an investment portfolio and its fluctuations is the core issue. Capital asset pricing model, arbitrage pricing theory, and Fama–French three-factor model were used to quantify the price of individual stocks and portfolios. Based on the second-order stochastic dominance rule, the higher moments of return series, the Shannon entropy, and some other actual investment constraints, we construct a multiconstraint portfolio optimization model, aiming at comprehensively weighting the returns and risk of portfolios rather than blindly maximizing its returns. Furthermore, the whale optimization algorithm based on FTSE100 index data is used to optimize the above multiconstraint portfolio optimization model, which significantly improves the rate of return of the simple diversified buy-and-hold strategy or the FTSE100 index. Furthermore, extensive experiments validate the superiority of the whale optimization algorithm over the other four swarm intelligence optimization algorithms (gray wolf optimizer, fruit fly optimization algorithm, particle swarm optimization, and firefly algorithm) through various indicators of the results, especially under harsh constraints.

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