scholarly journals Perturbed uncertain differential equations and perturbed reflected canonical process

2021 ◽  
Vol 6 (9) ◽  
pp. 9647-9659
Author(s):  
Yuanbin Ma ◽  
◽  
Zhi Li
Keyword(s):  
Differential Equations ◽  
Canonical Process

Uncertain Stochastic Option Pricing in the Presence of Uncertain Jumps

2019 ◽  
Vol 27 (04) ◽  
pp. 613-635
Author(s):  
Justin Chirima ◽  
Eriyoti Chikodza ◽  
Senelani Dorothy Hove-Musekwa
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Option Pricing ◽  
Stock Price ◽  
Call Option ◽  
Option Prices ◽  
Jump Size ◽  
Canonical Process ◽  
Option Pricing Model ◽  
Pricing Formula

In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty, is introduced and applied to describe the dynamics of a stock price process. This novel class of differential equations is called uncertain stochastic differential equations(USDES) with uncertain jumps. The existence and uniqueness theorem for this class of differential equations is proposed and proved. An appropriate version of the chain rule is derived and applied to solve some examples of USDES with uncertain jumps. The differential equation discussed is applied in an American call option pricing problem. In this problem, it is assumed that the evolution of the stock price is driven by a Brownian motion, the Liu canonical process and an uncertain renewal process. MATLAB is employed for implementing the derived option pricing model. Results show that option prices from the proposed call option pricing formula increase as the jump size increases. As compared to the proposed call option pricing formula, the Black-Scholes overprices options for a certain range of strike prices and under-prices the same options for another range of exercise prices when the jump size is zero.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

p-adic Differential Equations

2009 ◽  
Author(s):  
Kiran S. Kedlaya
Keyword(s):  
Differential Equations

Partial Differential Equations in Fluid Dynamics

2008 ◽  
Author(s):  
Isom H. Herron ◽  
Michael R. Foster
Keyword(s):  
Fluid Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

Differential Equations for Engineers

2009 ◽  
Author(s):  
Wei-Chau Xie
Keyword(s):  
Differential Equations

Product Integration with Application to Differential Equations

1984 ◽  
Author(s):  
John Day Dollard ◽  
Charles N. Friedman
Keyword(s):  
Differential Equations ◽  
Product Integration
Sign in / Sign up

Export Citation Format

Share Document