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Information-based approach:Pricing of a credit risky asset in the presence of default time

Probability, Uncertainty and Quantitative Risk 2024年第3期9卷 405-430页

作者： Mohammed Louriki Mathematics Department Faculty of Sciences SemalaliaCadi Ayyad UniversityBoulevard Prince Moulay AbdellahP.O.Bor 2390Marrakesh 40000Morocco

We extend the information-based asset-pricing framework by Brody,Hughston&Macrina to incorporate a stochastic bankruptcy time for the writer of the *** model introduces a non-defaultable cash flow Zr to be made at time T,alongside the time T of a possible bankruptcy of the writer of the asset are in line with the filtration generated by a Brownian random bridge with length v=T^T and pinning point ZT,where is a *** Z and T are not necessarily *** model does not depend crucially on the interpretation of as a bankruptcy *** derived the price process of the asset and compute the prices of associated *** dynamics of the price process satisfy a diffusion *** the approach of P.-***,we provide the explicit computation of the compensator of *** special properties of the bridge process,we also provide the explicit expression of the compensator of Zr I(v,+o).The resulting conclusion highlights the totally inaccessible property of the stopping time *** characteristic is particularly suitable for financial markets where the time of default of a writer cannot be predictable from any other signal in the system until default happens.

关键词： Brownian random bridge Semimartingale Local time Compensator process Information-based asset pricing Credit risk default time Totally inaccessible stopping time

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Constrained LQ Problem with a Random Jump and Application to Portfolio Selection

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Chinese Annals of Mathematics,Series B 2018年第5期39卷 829-848页

作者： Yuchao DONG Department of Mathematics Fudan University

This paper deals with a constrained stochastic linear-quadratic（LQ for short）optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Ito-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations（BSDEs for short）. The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.

关键词： Backward stochastic Riccati equation default time Mean-varianceproblem

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On the compensator of the default process in an information-based model

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 230-250页

作者： Matteo Ludovico Bedini Rainer Buckdahn Hans-Jurgen Engelbert Numerix MilanoItaly Universite de Bretagne Occidentale BrestFrance´School of MathematicsShandong UniversityJinanShandong ProvincePeople’s Republic of China Friedrich-Schiller-Universitat Fakult¨at f¨ur Mathematik und InformatikInstitut f¨ur StochastikJena¨Germany

This paper provides sufficient conditions for the time of bankruptcy(of a company or a state)for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval.

关键词： default time Totally inaccessible stopping time Brownian bridge on random intervals Local time Credit risk Compensator process

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