Dynamical analysis of rational and semi‐rational solution for a new extended (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation

Li, Lingfei; Yan, Yongsheng; Xie, Yingying

doi:10.1002/mma.8608

Cited by 4 publications

(1 citation statement)

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“…2. Next, based on the 2-soliton solution, we will construct the first order financial rogue wave solution of the generalized Black-Scholes equation (2.4) via the "long wave" limit [40,41]. Assuming p j , Ω j , ϕ j , η j are complex numbers, the 2-soliton solution can be expressed as…”

Section: -Soliton Solution and First Order Financial Rogue Wavementioning

confidence: 99%

Going beyond the Black-Scholes option pricing model: financial rogue waves in quantum mechanics

Li,

Zhu,

et al. 2024

Preprint

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This paper proposes a nonlinear alternative for the Black-Scholes option pricing model that is defined as the Gross-Pitaevskii equation. It models the controlled Brownian motion of the financial market and describes the option price wave function in terms of the compound price and time. Here, we analytically predict the existence of a family of financial rogue wave solutions of the Black-Scholes equation in the form of complex rational functions by introducing small perturbation and using symbolic computation. The obtained solutions compose of a single symmetric soliton or several solitary peaks. The existence of non-zero offset parameters provides nontrivial alterations to higher order solutions as they would decompose into first order ones that can be used to simulate the evolution of financial risks. Financial rogue wave demonstrates a condition that investors may face a huge risk or return in the financial market, which might be an actual theoretical basis for the existence of it. Our study is the first to give solid proof of the connection between option pricing and quantum mechanics. This finding opens a novel path for the excitation and control of financial waveforms of quantum mechanic footprint and extreme financial crisis.

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Section: -Soliton Solution and First Order Financial Rogue Wavementioning

confidence: 99%