On the Properties of Solution of Stochastic Differential Equation with Respect to Initial Data in One-dimensional Case
by
Fatima Benziadi
Vol. 15 No. 2 (2020) P.143~P.162
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DOI: | https://doi.org/10.21915/BIMAS.2020203 |
| | 10.21915/BIMAS.2020203 |
ABSTRACT
The one-default models are widely applied in modeling financial risk and in price valuation of financial products such as Credit default swap. In this paper, we are interested essentially to the so-called natural model. This model is expressed by a stochastic differential equation called $\natural$-equation, this equation displays the evolution of the defaultable market. So, on the same model and with some assumptions, we will study the property of homeomorphism of the stochastic flow generated by the natural model in a one-dimensional case and with some modifications, based on an important theory of Hiroshi Kunita. This is the main motivation of our research.
KEYWORDS
Credit risk, Stochastic flow, Stochastic diff erential geometry, Diff eomorphism
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60G17, 60H05
MILESTONES
Received: 2020-03-30
Revised :
Accepted: 2020-06-15
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