Mean-Variance-CvaR Model of Multiportfolio Optimization via Linear Weighted Sum Method

CVaR Robust Mean - CVaR Portfolio Optimization

One of the most important problems faced by every investor is asset allocation. An investor during making investment decisions has to search for equilibrium between risk and returns. Risk ‎and ‎return are uncertain parameters in ‎the ‎suggested portfolio optimization models and should be estimated to solve the‎problem. The estimation might‎ lead ‎to ‎large ‎error in the final decision. One of t...

Fast gradient descent method for Mean-CVaR optimization

We propose an iterative gradient descent procedure for computing approximate solutions for the scenario-based mean-CVaR portfolio selection problem. This procedure is based on an algorithm proposed by Nesterov [13] for solving non-smooth convex optimization problems. Our procedure does not require any linear programming solver and in many cases the iterative steps can be solved in closed form. ...

Adaptive Weighted Sum Method for Multiobjective Optimization

This paper presents an adaptive weighted sum method for multiobjective optimization problems. The authors developed the bi-objective adaptive weighted sum method, which determines uniformly-spaced Pareto optimal solutions, finds solutions on non-convex regions, and neglects non-Pareto optimal solutions. However, the method could solve only problems with two objective functions. In this work, th...

On variance reduction of mean-CVaR Monte Carlo estimators

Finite-sum Composition Optimization via Variance Reduced Gradient Descent

The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: minx (EiFi ◦ EjGj)(x). It summarizes many important applications in machine learning, statistics, and finance. In this paper, we consider the finite-sum scenario for composition optimization: min x f (x) := 1 n n ∑ i=1 Fi ( 1 m m ∑ j=1 Gj(x) ) . We pro...