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An optimal maintenance policy based on partial information
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
The inspection modeling approach to detect the system failure is similar to that of Ahmadi & Newby (2011) and Ahmadi & Wu (2017) assuming that inter-inspection times conform to a modulated Poisson process. Specifically, let N(t) be a modulated Poisson process such that N(t) with the associated time points of inspections, T1 < T2 < …, depicts the total number of arrivals up to time t. In other words, according to Aven and Jensen (Aven & Jensen 1998), N(t) admits a smooth semimartingale (SSM) with the ℱ-intensity λt, and the ℱ-martingale Mt: N(t)=∫0tλsds+Mt
The optimal investment strategy under the disordered return and random inflation
Published in Systems Science & Control Engineering, 2019
On the other hand, extending the random driving term from Brownian motion to martingale even to semimartingale, that will be applicability and generality of the model. For instance, Goll and Kallsen (2000) considered the logarithmic utility maximization problem from consumption or terminal net wealth in the semimartingale market model. Framstad, Øksendal, and Sulem (2001) considered the optimal consumption and investment when the risk asset price is semimartingale. Mania, Tevzadze, and Toronjadze (2008) considered the mean square hedging problem in which the asset price is driven by continuous semimartingale under partial information. Mania and Santacroce (2010) under partial information, assuming that the asset price was driven by semimartingale, studied the optimal investment strategy for maximizing the expected utility of terminal wealth. Li, Fei, Shi, and Li (2012, 2013) further studied optimal investment strategy with the disorder problem in the framework of semimartingale.