Work

Optimal Control in Financial Markets for the Uncertain Volatility Model

Year: 2025

Type: article

Abstract: This article generalizes the well-known Black-Scholes model, specifically the uncertain volatility model. To calculate the fair price range of a payment obligation, Hamilton-Jacobi-Bellman equations are derived and transformed into nonlinear heat equations with boundary conditions. Theorems are proven stating that, for a certain class of payment obligations, solutions to nonlinear heat equations satisfy the linear heat equations. A computational example using real data is provided.

Source: Mathematics

DOI: 10.3390/math14010003

Authors: Grigory Belyavski, Natalia Danilova, Irina Zemlyakova, Gennady Ougolnitsky

Institution: Southern Federal University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Russian Science Foundation