Journal of Applied Probability

The Markov consistency of Archimedean survival processes

J. Jakubowski and A. Pytel

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we connect Archimedean survival processes (ASPs) with the theory of Markov copulas. ASPs were introduced by Hoyle and Mengütürk (2013) to model the realized variance of two assets. We present some new properties of ASPs related to their dependency structure. We study weak and strong Markovian consistency properties of ASPs. An ASP is weak Markovian consistent, but generally not strong Markovian consistent. Our results contain necessary and sufficient conditions for an ASP to be strong Markovian consistent. These properties are closely related to the concept of Markov copulas, which is very useful in modelling different dependence phenomena. At the end we present possible applications.

Article information

Source
J. Appl. Probab., Volume 53, Number 2 (2016), 392-409.

Dates
First available in Project Euclid: 17 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1466172862

Mathematical Reviews number (MathSciNet)
MR3514286

Zentralblatt MATH identifier
1343.60111

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Keywords
Gamma random bridge Markovian consistency Archimedean survival process profitability

Citation

Jakubowski, J.; Pytel, A. The Markov consistency of Archimedean survival processes. J. Appl. Probab. 53 (2016), no. 2, 392--409. https://projecteuclid.org/euclid.jap/1466172862


Export citation

References

  • Abdel-Hameed, M. (1987). Inspection and maintenance policies of devices subject to deterioration. Adv. Appl. Prob. 19, 917–931.
  • Bielecki, T. R., Jakubowski, J. and Niew\kegłowski, M. (2012). Study of dependence for some stochastic processes: symbolic Markov copulae. Stoch. Process. Appl. 122, 930–951.
  • Bielecki, T. R., Jakubowski, J. and Niew\kegłowski, M. (2013). Intricacies of dependence between components of multivariate Markov chains: weak Markov consistency and weak Markov copulae. Electron. J. Prob. 18, 45.
  • Bielecki, T. R., Vidozzi, A. and Vidozzi, L. (2008). A Markov copulae approach to pricing and hedging of credit index derivatives and rating triggered step-up bonds. J. Credit Risk 4, 47–76.
  • Bielecki, T. R., Cousin, A., Crépey, S. and Herbertsson, A. (2014). Dynamic hedging of portfolio credit risk in a Markov copula model. J. Optimization Theory Appl. 161, 90–102.
  • Bielecki, T. R., Jakubowski, J., Vidozzi, A. and Vidozzi, L. (2008). Study of dependence for some stochastic processes. Stoch. Anal. Appl. 26, 903–924.
  • Dickson, D. C. M. and Waters, H. R. (1993). Gamma processes and finite time survival probabilities. ASTIN Bull. 23, 259–272.
  • Hoyle, E. and Mengütürk, L. A. (2013). Archimedean survival processes. J. Multivariate Anal. 115, 1–15.
  • Hoyle, E., Hughston, L. P. and Macrina, A. (2011). Lévy random bridges and the modelling of financial information. Stoch. Process. Appl. 121, 856–884.
  • Nelsen, R. B. (2006). An Introduction to Copulas, 2nd edn. Springer, New York.
  • Norberg, R. (1999). Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bull. 29, 5–27.
  • Van Noortwijk, J. M. (2009). A survey of the application of gamma processes in maintenance. Reliab. Eng. System Safety 94, 2–21.