Chance Constrained Robust Portfolio Optimization when the Perturbations Follow Normal and Exponential Distributions

TL;DR

This paper develops a method to transform uncertain portfolio optimization problems with stochastic parameters into deterministic, computationally manageable models, focusing on normal and exponential distribution-based uncertainties, and applies it to Indian stock data.

Contribution

It introduces a robust formulation for chance constrained portfolio optimization with normal and exponential perturbations, making the problem computationally tractable.

Findings

Robust counterparts are derived for normal and exponential perturbations.

The models are computationally tractable for quadratic programming problems.

Application to Indian stock market data demonstrates practical effectiveness.

Abstract

In this paper, we consider the chance constrained based uncertain portfolio optimization problem in which the uncertain parameters are stochastic in nature. The primary goal of the work is to formulate the uncertain problem into a deterministic model to study its robust counterpart, which will be helpful for solving such types of uncertain problems. In the present study, we assume that the uncertainty occurs in the expected asset returns, accordingly we derive the corresponding robust counterparts for the cases when the perturbations follow normal and exponential distributions. The obtained robust counterparts are computationally tractable. So our study can be used to find out the deterministic robust counterparts of any quadratic programming problems with uncertain constraints. In the end, we solve an Indian stock market problem for the nominal case as well as the cases for normally and exponentially distributed perturbations, and the results are analyzed.