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تسجيل مستخدم جديدThree essays on stopping
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تأليف
Eberhard Mayerhofer
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First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This modifies a formula by Perry et al (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for any drawdown threshold, if and only if the diffusion characteristic mu/sigma^2 is constant. This complements the sufficient condition formulated by Lehoczky (1977). Third, we give an alternative proof for the fact that the maximum at a fixed drawdown threshold is exponentially distributed for any spectrally negative Levy process, a result due to Mijatovic and Pistorius (2012).
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A collection of short expository essays by the author on various topics in quantum mechanics, quantum cosmology, and physics in general.
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In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We first const
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ometric properties of continuity or stopping regions. Especially, we make use of the concepts of convex sets and supporting hyperplane. Explicit formulae and efficiently computable bounds are obtained for average stopping times. Our techniques can be applied to bound average stopping times involving random vectors, nonlinear stopping boundary, and constraints of time indexes. Moreover, we establish a stochastic characteristic of convex sets and generalize Jensens inequality, Walds equations and Lordens inequality, which are useful for investigating average stopping times.
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