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A reading guide for last passage times with financial applications in view. (English) Zbl 1274.60123

The authors present a survey on last passage times in which they improve the previous results on this topic, relax the well-known assumptions and propose a unified approach that helps to recover many results for stochastic processes and mathematical finances. In order to study last passage times, a natural class of stochastic processes \(\sum\) is introduced. The processes from this class are uniquely characterized by a pair of a measure and the last zero. One of the new result is that any end of a predictable set that avoids stopping times can be written as the last time when a nonnegative local martingale having a continuous supremum process, starting at one and vanishing at infinity reaches its maximum. Some examples of explicit computations for the distribution of some last passage times are given. Financial applications are discussed.

MSC:

60G17 Sample path properties
60G44 Martingales with continuous parameter
91G20 Derivative securities (option pricing, hedging, etc.)
60G07 General theory of stochastic processes
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