Some Research Problems in Uncertainty Theory

By Baoding Liu. 2009

1,414 citations recorded by the source corpus.

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Citations in the corpus

Some formulas of variance of uncertain random variable (2014, background): “Besides, the product uncertain measure on the product σ -algebra L is defined by Liu [6] as follows: Axiom 4: (Product axiom) Let ( k ,Lk ,Mk) be uncertainty spaces for k = 1, 2, · · · .”
Asian Option Pricing Formula for Uncertain Financial Market (2015, background): “Based on the assumption that stock price follows a geometric Liu process, uncertainty theory was first introduced into finance by Liu [13] in 2009.”
Uncertain Programming Model for Chinese Postman Problem with Uncertain Weights (2012, methodology): “Later, in order to deal with differentiation and integration of functions of uncertain processes, uncertain calculus was initialized by Liu (2009a).”
Subadditivity of chance measure (2014, methodology): “After proposing the concept of independence [4], Liu [3] presented the operational law of uncertain variables.”
Expected Value of Function of Uncertain Variables (2010, background): “Furthermore, Liu [8] proposed uncertain inference that is a process of deriving consequences from uncertain knowledge or evidence via the tool of conditional uncertainty.”
A type of uncertain differential equations with analytic solution (2013, background): “Based on the canonical Liu process, Liu [10] proposed an uncertain integral of an uncertain process with respect to the canonical Liu process and thus founded a theory of uncertain calculus.”
A numerical method for solving uncertain differential equations (2013, methodology): “Liu [7] verified the fundamental theorem of uncertain calculus, i.”
A New Option Pricing Model for Stocks in Uncertainty Markets (2011, methodology): “(Liu (2009b)) An uncertain process t C is said to be a canonical process if (i) 0 0 C = and almost all sample paths are Lipschitz continuous, (ii) t C has stationary and independent increments, (iii) every increment sts CC + − is a normally distributed uncertain variable with expected value 0 and…”
A Transportation Problem with Uncertain Costs and Random Supplies (2015, methodology): “Uncertain measure M was introduced as a set function satisfying the following four axioms (Liu, 2007, 2009a): Axiom 1.”
Geometric Average Asian Option Pricing for Uncertain Financial Market (2014, background): “Different from Black-Scholes setting, Liu [7] supposed that the stock price follows an uncertain differential equation and presented an uncertain stock model in which the bond price Xt and the stock price St are determined by { dXt = rXtdt dSt = μStdt+ σStdCt (3.”
Uncertain programming model for uncertain optimal assignment problem (2013, methodology): “In financial mathematics, Liu [20] gave an uncertain stock model and a European option price formula.”
Existence and Uniqueness Theorem on Uncertain Dierential Equations with Local Lipschitz Condition (2012, unknown): “Definition 4 [9] An uncertain process Ct is said to be a canonical process if (i) C0 = 0 and almost all sample paths are Lipschitz continuous, (ii) Ct has stationary and independent increments, (iii) every increment Cs+t − Cs is a normal uncertain variable with expected value 0 and variance t(2).”
Uncertain Risk Analysis and Uncertain Reliability Analysis (2010, methodology): “In addition, Liu [8], Gao [3], You [15], Liu and Ha [13], and Peng and Iwamura [14] also made significant contributions to this research area.”
Uncertainty Theory (2004, unknown): “14 (Liu [80]) The uncertain variables ξ1, ξ2, · · · , ξn are said to be independent if”
Extreme values and integral of solution of uncertain differential equation (2013, methodology): “(Liu [10]) An uncertain process Ct is said to be a canonical Liu process if (i) C0 = 0 and almost all sample paths are Lipschitz continuous, (ii) Ct has stationary and independent increments, (iii) every increment Cs+t − Cs is a normal uncertain variable with expected value 0 and variance t2, whose ”
Toward uncertain finance theory (2013, methodology): “More precisely, an uncertain process Ct is called a canonical process by Liu [4] if (1) C0 = 0 and almost all sample paths are Lipschitz continuous, (2) Ct has stationary and independent increments, and (3) every increment Cs+t − Cs is a normal uncertain variable with expected value 0 and variance t”