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January  2017, 2: 10 doi: 10.1186/s41546-017-0017-4

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

Matteo Ludovico Bedini 1,, , Rainer Buckdahn 2,3, and  Hans-Jürgen Engelbert 4,

1 Numerix, Milano, Italy;

2 Université de Bretagne Occidentale, Brest, France;

3 School of Mathematics, Shandong University, Jinan, Shandong Province, People's Republic of China;

4 Friedrich-Schiller-Universität, Fakultät fär Mathematik und Informatik, Institut fär Stochastik, Jena, Germany

Received  November 18, 2016 Revised  April 18, 2017 Published  March 2017

Fund Project: supported by the European Community's FP 7 Program under contract PITN-GA-2008-213841, and Marie Curie ITN 《 Controlled Systems 》.

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.
Keywords: Default time, Totally inaccessible stopping time, Brownian bridge on random intervals, Local time, Credit risk, Compensator process.
Citation: Matteo Ludovico Bedini, Rainer Buckdahn, Hans-Jürgen Engelbert. On the compensator of the default process in an information-based model. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 10-. doi: 10.1186/s41546-017-0017-4
References:
[1]

Aven, T:A theorem for determining the compensator of a counting process. Scand. J. Stat 12, 62-72 (1985)

[2]

Bedini, ML:Information on a Default Time:Brownian Bridges on Stochastic Intervals and Enlargement of Filtrations. Dissertation, Friedrich-Schiller-Universität (2012)

[3]

Bedini, ML, Buckdahn, R, Engelbert, HJ:Brownian bridges on random intervals. Teor. Veroyatnost. i Primenen 61:1, 129-157 (2016)

[4]

Bedini, ML, Hinz, M:Credit default prediction and parabolic potential theory. Statistics & Probability Letters 124, 121-125 (2017)

[5]

Giesecke, K:Default and information. J. Econ. Dyn. Control 30, 2281-2303 (2006)

[6]

Jarrow, R, Protter, P:Structural versus Reduced Form Models:A New Information Based Perspective. J.Invest. Manag 2(2), 1-10 (2004). Second Quarter

[7]

Jeanblanc, M, Le Cam, Y:Progressive enlargement of filtrations with initial times. Stoch. Proc. Appl. 119(8), 2523-2543 (2009)

[8]

Jeanblanc, M, Le Cam, Y:Immersion property and Credit Risk Modelling. In:Delbaen, F, Miklós, Kallenberg, O Foundations of Modern Probability, Second edition. Springer-Verlag, New-York (2002)

[9]

Karatzas, I, Shreve, S Brownian Motion and Stochastic Calculus, Second edition. Springer-Verlag, Berlin(1991)

[10]

Meyer, PA:Probability and Potentials. Blaisdail Publishing Company, London (1966)

[11]

Revuz, D, Yor, M Continuous Martingales and Brownian Motion, Third edition. Springer-Verlag, Berlin(1999)

[12]

Rogers, LCG, Williams, D Diffusions, Markov Processes and Martingales. Vol. 2:Itô Calculus, Second edition. Cambridge University Press, Cambridge (2000)

show all references

References:
[1]

Aven, T:A theorem for determining the compensator of a counting process. Scand. J. Stat 12, 62-72 (1985)

[2]

Bedini, ML:Information on a Default Time:Brownian Bridges on Stochastic Intervals and Enlargement of Filtrations. Dissertation, Friedrich-Schiller-Universität (2012)

[3]

Bedini, ML, Buckdahn, R, Engelbert, HJ:Brownian bridges on random intervals. Teor. Veroyatnost. i Primenen 61:1, 129-157 (2016)

[4]

Bedini, ML, Hinz, M:Credit default prediction and parabolic potential theory. Statistics & Probability Letters 124, 121-125 (2017)

[5]

Giesecke, K:Default and information. J. Econ. Dyn. Control 30, 2281-2303 (2006)

[6]

Jarrow, R, Protter, P:Structural versus Reduced Form Models:A New Information Based Perspective. J.Invest. Manag 2(2), 1-10 (2004). Second Quarter

[7]

Jeanblanc, M, Le Cam, Y:Progressive enlargement of filtrations with initial times. Stoch. Proc. Appl. 119(8), 2523-2543 (2009)

[8]

Jeanblanc, M, Le Cam, Y:Immersion property and Credit Risk Modelling. In:Delbaen, F, Miklós, Kallenberg, O Foundations of Modern Probability, Second edition. Springer-Verlag, New-York (2002)

[9]

Karatzas, I, Shreve, S Brownian Motion and Stochastic Calculus, Second edition. Springer-Verlag, Berlin(1991)

[10]

Meyer, PA:Probability and Potentials. Blaisdail Publishing Company, London (1966)

[11]

Revuz, D, Yor, M Continuous Martingales and Brownian Motion, Third edition. Springer-Verlag, Berlin(1999)

[12]

Rogers, LCG, Williams, D Diffusions, Markov Processes and Martingales. Vol. 2:Itô Calculus, Second edition. Cambridge University Press, Cambridge (2000)

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