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New Analytical Solution for Optimizing Portfolios With Value-At-Risk Constraints

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New research has made progress in solving a long-standing problem in the banking and insurance sectors. The study, titled "Value-at-risk Constrained Portfolios in Incomplete Markets: A Dynamic Programming Approach to Heston's Model," explores the optimization of portfolio investments under Value-at-Risk (VaR) constraints in the presence of stochastic volatility.

The major breakthrough of this research is the development of an analytical solution to maximize expected utility while complying with VaR constraints on terminal wealth. This has been a challenging problem due to the time-dependent volatilities observed in financial markets and the regulatory requirements placed on financial institutions.

The study demonstrates that the optimal investment strategy can be derived using dynamic programming techniques. It establishes a link between the constrained optimization problem and the unconstrained one through the use of a synthetic derivative. This innovation allows for the calculation of optimal allocation in the presence of VaR constraints.

Numerical studies conducted by the researchers highlight the impact of risk aversion levels and investment horizons on the optimal investment strategy. Notably, for investors with low risk aversion and short investment horizons, there can be a significant difference of up to 20% between the constrained and unconstrained allocations.

The findings of this study have important implications for the banking and insurance sectors. By providing a solution to the optimization problem under VaR constraints, financial institutions can enhance their risk management practices and ensure compliance with regulatory requirements. This research opens up avenues for further exploration, such as applying the methodology to other incomplete market problems or different types of constraints.

Overall, this research represents a significant advancement in portfolio optimization under VaR constraints. Its practical implications make it valuable for financial professionals and researchers in the field. With its analytical solution and numerical insights, this study contributes to the understanding and effective management of risk in financial markets.

Research in English does not provide investment or financial advice. This article is provided for information purposes only.

Tags: Economics | Economics:Finance | Math

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