scholarly journals On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models

2017 ◽  
Vol 121 ◽  
pp. 152-162 ◽  
Author(s):  
Pavel V. Gapeev ◽  
Yavor I. Stoev
Keyword(s):  
Jump Diffusion ◽  
Laplace Transforms ◽  
Diffusion Models ◽  
Exit Times ◽  
One Dimensional ◽  
First Exit Times

SOME REMARKS ON MEAN-VARIANCE HEDGING FOR DISCONTINUOUS ASSET PRICE PROCESSES

2005 ◽  
Vol 08 (04) ◽  
pp. 425-443 ◽  
Author(s):  
TAKUJI ARAI
Keyword(s):  
Asset Price ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Continuous Case ◽  
Martingale Measure ◽  
Trade Off ◽  
One Dimensional ◽  
The Mean ◽  
Duality Approach ◽  
Mean Variance

Mean-variance hedging for the discontinuous semimartingale case is obtained under some assumptions related to the variance-optimal martingale measure. In the present paper, two remarks on it are discussed. One is an extension of Hou–Karatzas' duality approach from the continuous case to discontinuous. Another is to prove that there is the consistency with the case where the mean-variance trade-off process is continuous and deterministic. In particular, one-dimensional jump diffusion models are discussed as simple examples.

scholarly journals Exact simulation of first exit times for one-dimensional diffusion processes

2020 ◽  
Vol 54 (3) ◽  
pp. 811-844
Author(s):  
Samuel Herrmann ◽  
Cristina Zucca
Keyword(s):  
Diffusion Processes ◽  
Exit Time ◽  
Convergent Series ◽  
Mathematical Finance ◽  
Exit Times ◽  
Rejection Sampling ◽  
Girsanov Transformation ◽  
One Dimensional ◽  
Usual Procedure ◽  
First Exit Times

The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability… The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.

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