Boundary crossing probabilities for (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:math>)-Slepian-processes

Bischoff, Wolfgang; Gegg, Andreas

doi:10.1016/j.spl.2016.06.023

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Cited by 4 publications

References 18 publications

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First passage times for Slepian process with linear and piecewise linear barriers

Zhigljavsky

Noonan

2021

Extremes

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In this paper, we derive explicit formulas for the first-passage probabilities of the process S(t) = W(t) − W(t + 1), where W(t) is the Brownian motion, for linear and piece-wise linear barriers on arbitrary intervals [0,T]. Previously, explicit formulas for the first-passage probabilities of this process were known only for the cases of a constant barrier or T ≤ 1. The first-passage probabilities results are used to derive explicit formulas for the power of a familiar test for change-point detection in the Wiener process.

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First passage times for Slepian process with linear and piecewise linear barriers

Zhigljavsky

Noonan

2021

Extremes

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The Joint Distribution of Running Maximum of a Slepian Process

Deng

2017

Methodol Comput Appl Probab

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Consider the Slepian process S defined by S(t) = B(t + 1) − B(t), t ∈ [0, 1] with B(t), t ∈ R a standard Brownian motion. In this contribution we analyze the joint distribution between the maximum m s = max 0≤u≤s S(u) certain and the maximum M t = max 0≤u≤t S(u) for 0 < s < t fixed. Explicit integral expression are obtained for the distribution function of the partial maximum m s and the joint distribution function between m s and M t . We also use our results to determine the moments of m s .

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Barrier Options Pricing With Joint Distribution of Gaussian Process and Its Maximum

Deng

2017

Int. J. Theor. Appl. Finan.

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Barrier options are one of the most popular exotic options. In this contribution, we propose a performance barrier option, which is a type of barrier option defined with the [Formula: see text]th period logarithm return rate process on an underlying asset over the time interval [Formula: see text], [Formula: see text]. We show that the price of this performance barrier option is determined by the joint distribution of a Slepian process and its maximum. Furthermore, we derive a tractable formula for this joint distribution and obtain explicit formulas for the up-out-call performance option and up-out-put performance option.

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Boundary crossing probabilities for (q,d)-Slepian-processes

Cited by 4 publications

References 18 publications

First passage times for Slepian process with linear and piecewise linear barriers

First passage times for Slepian process with linear and piecewise linear barriers

The Joint Distribution of Running Maximum of a Slepian Process

Barrier Options Pricing With Joint Distribution of Gaussian Process and Its Maximum

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