Benth, F.E. and Pircalabu, A. (2022) On Jump-Diffusion Processes in Option Pricing. Finance and Stochastics.

has been cited by the following article:

• TITLE: Real Options Assessment in the Time-Fractional Heston Model with Jump and Inertia

  AUTHORS: Ngoyi Landu Tresor, René Gilles Bokolo, Mabela Rostin, Walo Omana

  KEYWORDS: Real Options, Time-Fractional Heston Model, Jump, Inertia, Stopping Times, Caputo Fractional Derivative, Viscosity Solutions

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.6, June 12, 2025

  ABSTRACT: This research addresses the assessment of real options via the time-fractional Heston model, which takes into account jumps and inertia. First, we examine the existence and uniqueness of viscosity solutions leveraging the continuous model reformulated as a time-fractional Hamilton-Jacobi-Bellman (HJB) equation using Caputo fractional derivative and Rellich-Kondrachov compactness theorem. Secondly, we present a higher-order regularity result stylized with Sobolev embeddings and Caputo fractional derivative expressed using the Duhamel principle. Third, we investigate some well-known discrete approaches proving the backward martingale convergence theorem with the Caputo time-fractional derivative being approximated using the Grünwald-Letnikov scheme. Finally, we show the existence of Nash-equilibrium solution for the pricing of real options with both two players and two stopping times, which results in lengthy implications for risk management and strategic decision making.