Discrete Bismut formula: Conditional integration by parts and a representation for delta hedging process

2021 ◽  
pp. 1-9
Author(s):  
Naho Akiyama ◽  
Toshihiro Yamada
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Malliavin Calculus ◽  
Random Walk Model ◽  
Integration By Parts ◽  
Exponential Process ◽  
Malliavin Derivative ◽  
Integration By Parts Formula ◽  
Delta Hedging ◽  
New Formula

The paper gives discrete conditional integration by parts formula using a Malliavin calculus approach in discrete-time setting. Then the discrete Bismut formula is introduced for asymmetric random walk model and asymmetric exponential process. In particular, a new formula for delta hedging process is obtained as an extension of the Malliavin derivative representation of the delta where the conditional integration by parts formula plays a role in the proof.

scholarly journals Integration by parts formula for SPDEs with multiplicative noise and its applications

2019 ◽  
Vol 19 (03) ◽  
pp. 1950024
Author(s):  
Xing Huang ◽  
Li-Xia Liu ◽  
Shao-Qin Zhang
Keyword(s):  
Probability Measure ◽  
Malliavin Calculus ◽  
Multiplicative Noise ◽  
Logarithmic Derivative ◽  
Transition Probability ◽  
Spin Systems ◽  
Integration By Parts ◽  
Discrete Lattices ◽  
Integration By Parts Formula

By using the Malliavin calculus, the Driver-type integration by parts formula is established for the semigroup associated to SPDEs with Multiplicative Noise. Moreover, estimates on the logarithmic derivative of the transition probability measure are obtained. A concrete example to describe evolution of spin systems on discrete lattices is given to illustrate our main result.

AN IMPROVEMENT OF MARKOVIAN INTEGRATION BY PARTS FORMULA AND APPLICATION TO SENSITIVITY COMPUTATION

2021 ◽  
pp. 1-21
Author(s):  
Yue Liu ◽  
Zhiyan Shi ◽  
Ying Tang ◽  
Jingjing Yao ◽  
Xincheng Zhu
Keyword(s):  
Perturbation Analysis ◽  
Malliavin Calculus ◽  
Transition Rate ◽  
Infinitesimal Perturbation Analysis ◽  
Analysis Method ◽  
Rate Matrix ◽  
Integration By Parts ◽  
Transition Rate Matrix ◽  
Integration By Parts Formula ◽  
Infinitesimal Perturbation

This paper establishes a new version of integration by parts formula of Markov chains for sensitivity computation, under much lower restrictions than the existing researches. Our approach is more fundamental and applicable without using Girsanov theorem or Malliavin calculus as did by past papers. Numerically, we apply this formula to compute sensitivity regarding the transition rate matrix and compare with a recent research by an IPA (infinitesimal perturbation analysis) method and other approaches.

A discrete time random walk model for anomalous diffusion

2015 ◽  
Vol 293 ◽  
pp. 53-69 ◽  
Author(s):  
C.N. Angstmann ◽  
I.C. Donnelly ◽  
B.I. Henry ◽  
J.A. Nichols
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Anomalous Diffusion ◽  
Random Walk Model

A Multi-Label Classification Algorithm Based on Random Walk Model

2010 ◽  
Vol 33 (8) ◽  
pp. 1418-1426 ◽  
Author(s):  
Wei ZHENG ◽  
Chao-Kun WANG ◽  
Zhang LIU ◽  
Jian-Min WANG
Keyword(s):  
Random Walk ◽  
Classification Algorithm ◽  
Random Walk Model

scholarly journals On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

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