• Previous Article
    The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks
  • PUQR Home
  • This Issue
  • Next Article
    Characterization of optimal feedback for stochastic linear quadratic control problems
January  2017, 2: 10 doi: 10.1186/s41546-017-0017-4

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

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

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.
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) Google Scholar

[2]

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

[3]

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

[4]

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

[5]

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

[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 Google Scholar

[7]

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

[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) Google Scholar

[9]

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

[10]

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

[11]

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

[12]

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

show all references

References:
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[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 Google Scholar

[7]

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

[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) Google Scholar

[9]

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

[10]

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

[11]

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

[12]

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

[1]

Anna Maria Cherubini, Giorgio Metafune, Francesco Paparella. On the stopping time of a bouncing ball. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 43-72. doi: 10.3934/dcdsb.2008.10.43

[2]

Qingwu Gao, Zhongquan Huang, Houcai Shen, Juan Zheng. Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims. Journal of Industrial & Management Optimization, 2016, 12 (1) : 31-43. doi: 10.3934/jimo.2016.12.31

[3]

Baoyin Xun, Kam C. Yuen, Kaiyong Wang. The finite-time ruin probability of a risk model with a general counting process and stochastic return. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021032

[4]

Yoshikazu Giga, Hirotoshi Kuroda. A counterexample to finite time stopping property for one-harmonic map flow. Communications on Pure & Applied Analysis, 2015, 14 (1) : 121-125. doi: 10.3934/cpaa.2015.14.121

[5]

Gongwei Liu, Baowei Feng, Xinguang Yang. Longtime dynamics for a type of suspension bridge equation with past history and time delay. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4995-5013. doi: 10.3934/cpaa.2020224

[6]

Yuebao Wang, Qingwu Gao, Kaiyong Wang, Xijun Liu. Random time ruin probability for the renewal risk model with heavy-tailed claims. Journal of Industrial & Management Optimization, 2009, 5 (4) : 719-736. doi: 10.3934/jimo.2009.5.719

[7]

Rongfei Liu, Dingcheng Wang, Jiangyan Peng. Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival times. Journal of Industrial & Management Optimization, 2017, 13 (2) : 995-1007. doi: 10.3934/jimo.2016058

[8]

Puspita Mahata, Gour Chandra Mahata. Two-echelon trade credit with default risk in an EOQ model for deteriorating items under dynamic demand. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020138

[9]

Xiaoshan Chen, Xun Li, Fahuai Yi. Optimal stopping investment with non-smooth utility over an infinite time horizon. Journal of Industrial & Management Optimization, 2019, 15 (1) : 81-96. doi: 10.3934/jimo.2018033

[10]

Suping Wang, Qiaozhen Ma. Existence of pullback attractors for the non-autonomous suspension bridge equation with time delay. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1299-1316. doi: 10.3934/dcdsb.2019221

[11]

Simone Göttlich, Stephan Martin, Thorsten Sickenberger. Time-continuous production networks with random breakdowns. Networks & Heterogeneous Media, 2011, 6 (4) : 695-714. doi: 10.3934/nhm.2011.6.695

[12]

Janusz Mierczyński, Wenxian Shen. Time averaging for nonautonomous/random linear parabolic equations. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 661-699. doi: 10.3934/dcdsb.2008.9.661

[13]

Yinhua Xia, Yan Xu, Chi-Wang Shu. Efficient time discretization for local discontinuous Galerkin methods. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 677-693. doi: 10.3934/dcdsb.2007.8.677

[14]

Emilija Bernackaitė, Jonas Šiaulys. The finite-time ruin probability for an inhomogeneous renewal risk model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 207-222. doi: 10.3934/jimo.2016012

[15]

Abhyudai Singh, Roger M. Nisbet. Variation in risk in single-species discrete-time models. Mathematical Biosciences & Engineering, 2008, 5 (4) : 859-875. doi: 10.3934/mbe.2008.5.859

[16]

Tomasz R. Bielecki, Igor Cialenco, Marcin Pitera. A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 3-. doi: 10.1186/s41546-017-0012-9

[17]

Reza Lotfi, Zahra Yadegari, Seyed Hossein Hosseini, Amir Hossein Khameneh, Erfan Babaee Tirkolaee, Gerhard-Wilhelm Weber. A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020158

[18]

Shulin Wang, Yangrong Li. Probabilistic continuity of a pullback random attractor in time-sample. Discrete & Continuous Dynamical Systems - B, 2020, 25 (7) : 2699-2772. doi: 10.3934/dcdsb.2020028

[19]

Fritz Colonius, Guilherme Mazanti. Decay rates for stabilization of linear continuous-time systems with random switching. Mathematical Control & Related Fields, 2019, 9 (1) : 39-58. doi: 10.3934/mcrf.2019002

[20]

Pablo D. Carrasco, Túlio Vales. A symmetric Random Walk defined by the time-one map of a geodesic flow. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2891-2905. doi: 10.3934/dcds.2020390

 Impact Factor: 

Metrics

  • PDF downloads (8)
  • HTML views (137)
  • Cited by (0)

[Back to Top]