Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

A maximum principle for a stochastic control problem with multiple random terminal times

Department of Computer Science, University of Verona, Strada le Grazie, 15, Verona, 37134, Italy

In the present paper we derive, via a backward induction technique, an ad hoc maximum principle for an optimal control problem with multiple random terminal times. We thus apply the aforementioned result to the case of a linear quadratic controller, providing solutions for the optimal control in terms of Riccati backward SDE with random terminal time.
  Article Metrics


1. Barbu V, Cordoni F, Di Persio L (2016) Optimal control of stochastic FitzHugh-Nagumo equation. Int J Control 89: 746-756.    

2. Bielecki TR, Jeanblanc M, Rutkowski M (2004) Modeling and Valuation of Credit Risk, In: Stochastic Methods in Finance, Berlin: Springer, 27-126.

3. Bielecki TR, Rutkowski M (2013) Credit Risk: Modeling, Valuation and Hedging, Springer Science & Business Media.

4. Capponi A, Chen PC (2015) Systemic risk mitigation in financial networks. J Econ Dynam Control 58: 152-166.    

5. Cordoni F, Di Persio L (2016) A BSDE with delayed generator approach to pricing under counterparty risk and collateralization. Int J Stoch Anal 2016: 1-10.

6. Cordoni F, Di Persio L (2017) Gaussian estimates on networks with dynamic stochastic boundary conditions. Infin Dimens Anal Qu 20: 1750001.    

7. Cordoni F, Di Persio L (2017) Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions. J Math Anal Appl 451: 583-603.    

8. Cordoni F, Di Persio L, Prezioso L. A lending scheme for a system of interconnected banks with probabilistic constraints of failure. Available from: https://arxiv.org/abs/1903.06042.

9. Di Persio L, Ziglio G (2011) Gaussian estimates on networks with applications to optimal control. Net Het Media 6: 279-296.

10. Eisenberg L, Noe TH (2001) Systemic risk in financial systems. Manage Sci 47: 236-249.    

11. El Karoui N, Jeanblanc M, Jiao Y (2010) What happens after a default: The conditional density approach. Stoch Proc Appl 120: 1011-1032.    

12. Fleming WH, Soner HM (2006) Controlled Markov Processes and Viscosity Solutions, Springer Science & Business Media.

13. Guatteri G, Tessitore G (2008) Backward stochastic Riccati equations and infinite horizon LQ optimal control with infinite dimensional state space and random coefficients. Appl Math Opt 57: 207-235.    

14. Guatteri G, Tessitore G (2005) On the backward stochastic Riccati equation in infinite dimensions. SIAM J Control Opt 44: 159-194.    

15. Hurd TR (2015) Contagion! The Spread of Systemic Risk in Financial Networks, Springer.

16. Kohlmann M, Zhou XY (2000) Relationship between backward stochastic differential equations and stochastic controls: A linear-quadratic approach. SIAM J Control Opt 38: 1392-1407.    

17. Kohlmann M, Tang S (2002) Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging. Stoch Proc Appl 97: 255-288.    

18. Ying J, Kharroubi I, Pham H (2013). Optimal investment under multiple defaults risk: A BSDEdecomposition approach. Ann Appl Probab 23: 455-491.    

19. Lipton A (2016) Modern monetary circuit theory, stability of interconnected banking network, and balance sheet optimization for individual banks. Int J Theor Appl Financ 19: 1650034.    

20. Mansuy R, Yor M (2006) Random Times and Enlargements of Filtrations in a Brownian Setting, Berlin: Springer.

21. Merton RC (1974) On the pricing of corporate debt: The risk structure of interest rates. J financ 29: 449-470.

22. Mou L, Yong J (2007) A variational formula for stochastic controls and some applications. Pure Appl Math Q 3: 539-567.    

23. Pham H (2010) Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management. Stoch Proc Appl 120: 1795-1820.    

24. Pham H (2009) Continuous-Time Stochastic Control and Optimization with Financial Applications, Springer Science & Business Media.

25. Pham H (2005) On some recent aspects of stochastic control and their applications. Probab Surv 2: 506-549.    

26. Tang S (2003) General linear quadratic optimal stochastic control problems with random coefficients: Linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J Control Opt 42: 53-75.    

27. Yong J, Zhou XY (1999) Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer Science & Business Media.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved