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A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 35-86页

作者： Tomasz R.Bielecki Igor Cialenco M.Pitera Department of Applied Mathematics Illinois Institute of Technology10 W 32nd StrBuilding E1Room 208ChicagoIL 60616USA Institute of Mathematics Jagiellonian UniversityCracowPoland

In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time *** two key operational concepts used throughout are the notion of the LMmeasure and the notion of the update rule that,we believe,are the key tools for studying time consistency in a unified framework.

关键词： Time consistency update rule Dynamic LM-measure Dynamic risk measure Dynamic acceptability index Measure of performance

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Approximating Ordinary Differential Equations by Means of the Chess Game Moves

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Journal of Applied Mathematics and Physics 2022年第10期10卷 3240-3263页

作者： Maria Teresa Signes-Pont Joan Boters-Pitarch José Juan Cortés-Plana Higinio Mora-Mora Department of Computer Science and Technology University of Alicante Alicante Spain

The chess game provides a very rich experience in neighborhood types. The chess pieces have vertical, horizontal, diagonal, up/down or combined movements on one or many squares of the chess. These movements can associate with neighborhoods. Our work aims to set a behavioral approximation between calculations carried out by means of traditional computation tools such as ordinary differential equations (ODEs) and the evolution of the value of the cells caused by the chess game moves. Our proposal is based on a grid. The cells’ value changes as time pass depending on both their neighborhood and an update rule. This framework succeeds in applying real data matching in the cases of the ODEs used in compartmental models of disease expansion, such as the well-known Susceptible-Infected Recovered (SIR) model and its derivatives, as well as in the case of population dynamics in competition for resources, depicted by the Lotke-Volterra model.

关键词： Chess Game Neighborhood update rule ODE SIR Model Lotke-Volterra Model

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