Springer

  • This authored monograph covers a viability to approach to  traffic management by advising to vehicles circulated on the network the velocity they should follow for satisfying global traffic conditions;. It presents an investigation of three structural innovations:
     
    The objective is to broadcast at each instant and at each position the advised celerity to vehicles, which could be read by auxiliary speedometers or used by cruise control devices.
     
    Namely, 
    1. Construct regulation feedback providing at each time and position advised velocities (celerities)   for minimizing congestion or other requirements.
    2. Taking into account traffic constraints of different type, the first one being to remain on the roads, to stop at junctions, etc.
    3. Use information provided by the probe vehicles equipped with GPS to the traffic regulator;
    4. Use other global traffic measures of vehicles provided by different types of sensors;
     
    These results are based on convex analysis, intertemporal optimization and viability theory as mathematical tools as well as viability algorithms on the computing side, instead of conventional techniques such as partial differential equations and their resolution by finite difference or finite elements algorithms. The target audience primarily covers researchers and mathematically oriented engineers but the book may also be beneficial for graduate students.

  • Time and Money

    Jean Pierre Aubin

    This authored monograph presents an unconventional approach to an important topic in economic theory. The author is an expert in the field of viability theory and applies this theory to analyze how an economy should be dynamically endowed so that it is economically viable. Economic viability requires an assumption on the joint evolution of transactions, fluctuations of prices and units of numeraire goods: the sum of the "transactions values" and the "impact of price fluctuations" should be negative or equal to zero. The book presents a computation of the minimum endowment which restores economic viability and derives the dynamic laws that regulate both transactions and price fluctuations.
    The target audience primarily comprises open-minded and mathematically interested economists but the book may also be beneficial for graduate students.

  • This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term "tychastic viability measure of risk" is an evolutionary alternative to statistical measures, when dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners.

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