Toward uncertain finance theory

By Baoding Liu. 2013

310 citations recorded by the source corpus.

This paper first introduces a paradox of stochastic finance theory that shows the real stock price is impossible to follow any Ito’s stochastic differential equation. After a survey on uncertainty theory, uncertain process, uncertain calculus, and uncertain differential equation, this paper discusses some possible applications of uncertain differential equations to financial markets. Finally, it is suggested that a new uncertain finance theory should be developed based on uncertainty theory and uncertain differential equation.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bbee73d722d81f12cda55aec436a4b114a351200

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Citations in the corpus

Uncertain fractional differential equations and an interest rate model (2015, background): “Canonical process is a basic concept in uncertainty theory, which was established by Liu in 2007 [22] and refined in 2010 [23].”
Liu process and uncertain calculus (2013, background): “Liu [24] discussed some basic concepts of uncertain finance.”
Existence and uniqueness of the solution to uncertain fractional differential equation (2015, methodology): “The uncertain differential equation has been applied in some fields such as uncertain finance [29], uncertain optimal control [30], and uncertain differential game [31].”
Uncertain differential games with application to capitalism (2013, unknown): “As an application of uncertain differential equation, Liu [22] presented a paradox of stochastic finance theory which showed that the real stock price was impossible to follow any Ito’s stochastic differential equation, and suggested a new uncertain finance theory which was described by an uncertain”
Subadditivity of chance measure (2014, background): “Liu [9] introduced a paradox of stochastic finance theory based on uncertainty theory and uncertain differential equation.”
A type of uncertain differential equations with analytic solution (2013, background): “For more recent developments in uncertain finance, please refer to Liu [24].”
Runge-Kutta Method for Solving Uncertain Differential Equations (2015, background): “Uncertain differential equations have been widely applied in many fields such as uncertain finance (Liu [7], Yao [8]), uncertain optimal control (Zhu [9]), and uncertain differential game (Yang and Gao [10]).”
Extreme values and integral of solution of uncertain differential equation (2013, background): “Due to the paradox of stochastic finance theory (Liu [22]), Liu [10] presented an uncertain stock model via uncertain differential equation, and gave its European option pricing formulas, opening the door of uncertain finance theory.”