Comparison of various risk measures for an optimal portfolio

TL;DR

This paper compares different risk measures like VaR, Expected Loss, and Utility Loss for optimal portfolio selection under the Black-Scholes model, providing closed-form solutions and numerical comparisons.

Contribution

It introduces a method to derive closed-form solutions for optimal portfolios using various risk measures and compares their performance in a unified framework.

Findings

Different risk measures lead to distinct optimal strategies.

Numerical results highlight the trade-offs among risk measures.

The approach facilitates future research in risk-aware portfolio optimization.

Abstract

In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected Loss and Expected Utility Loss measures. To do so, under the Black- Scholes model for the financial market, Martingale method is applied to give closed-form solutions for the optimal terminal wealths; then via representation problem the optimal portfolio strategies are achieved. We compare the performances of these measures on the terminal wealths and optimal strategies of such constrained investors. Finally, we present some numerical results to compare them in several respects to give light to further studies.