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01.07.2015 | Methodologies and Application

Uncertain differential equation with jumps

verfasst von: Kai Yao

Erschienen in: Soft Computing | Ausgabe 7/2015

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Abstract

Uncertain differential equation is a type of differential equation driven by a canonical Liu process. Traditional uncertain differential equation can only deal with a continuous dynamic uncertain system. To model the sharp drifts embedded in an uncertain dynamic system, this paper proposes a type of uncertain differential equation driven by a canonical Liu process and an uncertain renewal process, which is called an uncertain differential equation with jumps. A sufficient condition for the proposed equation having a unique solution is first given, then a concept of stability for the proposed equation is provided in the sense of uncertain measure, and its sufficient condition is also derived.

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Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Politi Econ 81:637–654MATHCrossRef

Chen X, Liu B (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Mak 9(1):69–81MATHMathSciNetCrossRef

Chen X (2011) American option pricing formula for uncertain financial market. Int J Oper Res 8(2):32–37

Chen X, Ralescu DA (2013) Liu process and uncertain calculus. J Uncertain Anal Appl 1(3)

Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604MATHMathSciNetCrossRef

Gao Y (2012) Existence and uniqueness theorem on uncertain differential equations with local Lipschitz condition. J Uncertain Syst 6(3):223–232

Gao Y, Yao K (2014) Continuous dependence theorems on solutions of uncertain differential equations. App Math Modell 38:3031–3037MathSciNetCrossRef

Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. J Basic Eng 83:95–108MathSciNetCrossRef

Liu B (2007) Uncertain Theory, 2nd edn. Springer, Berlin

Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3–16

Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRef

Liu B, Yao K (2012) Uncertain integral with respect to multiple canonical processes. J Uncertain Syst 6(4):250–255

Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1(1)

Liu YH (2012) An analytic method for solving uncertain differential equations. J Uncertain Syst 6(4):244–249

Liu YH, Chen X, Ralescu DA (2014) Uncertain currency model and currency option pricing. Int J Intell Syst, to be published

Yao K (2012) Uncertain calculus with renewal process. Fuzzy Optim Decis Mak 11(3):285–297MATHMathSciNetCrossRef

Yao K, Li X (2012) Uncertain alternating renewal process and its application. IEEE Transa Fuzzy Syst 20(6):1154–1160MathSciNetCrossRef

Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):3–13MathSciNetCrossRef

Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832MATHMathSciNet

Yao K (2013) Extreme values and integral of solution of uncertain differential equation. J Uncertain Anal Appl 1(2)

Yao K (2013) A type of nonlinear uncertain differential equations with analytic solution. J Uncertain Anal Appl 1(8)

Zhang XF, Ning YF, Meng GW (2013) Delayed renewal process with uncertain interarrival times. Fuzzy Optim Decis Mak 12(1):79–87MathSciNetCrossRef

Titel: Uncertain differential equation with jumps
verfasst von: Kai Yao
Publikationsdatum: 01.07.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 7/2015
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-014-1392-8

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