Skip to main content
SpringerLink
Log in

Jump-diffusion asset–liability management via risk-sensitive control

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

In this paper, we use risk-sensitive control methods to solve a jump-diffusion asset–liability management (ALM) problem. We show that the ALM problem admits a unique classical (\(C^{1,2}\)) solution under two different sets of assumptions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barles G, Imbert C (2008) Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited. Annales de l’Institut Henri Poincaré 25(3):567–585

    Google Scholar 

  • Bellman R (1957) Dynamic programming. Princeton University Press, Princeton

    Google Scholar 

  • Benk M (2012) Intertemporal surplus management with jump risk. In: Gassmann HI, Ziemba WT (eds) Stochastic programming: applications in finance, energy, planning and logistics, vol 4. World Scientific Publishing Company, World Scientific Series in Finance, pp 69–96

  • Bielecki T, Pliska S (1999) Risk-sensitive dynamic asset management. Appl Math Optim 39:337–360

    Article  Google Scholar 

  • Bouchard B, Touzi N (2011) Weak dynamic programming principle for viscosity solutions. SIAM J Control Optim 49:948–962

    Article  Google Scholar 

  • Crandall M, Ishii H, Lions PL (1992) User’s guide to viscosity solutions of second order partial differential equations. Bull Am Math Soc 27(1):1–67

    Article  Google Scholar 

  • Davis M, Lleo S (2010) Risk-sensitive asset management and affine processes. In: Kijima M, Hara C, Tanaka K, Muromachi Y (eds) KIER-TMU International Workshop on Financial Engineering 2009, World Scientific, pp 1–43

  • Davis M, Lleo S (2011) Jump-diffusion risk-sensitive asset management I: diffusion factor model. SIAM J Financ Math 2:22–54

    Article  Google Scholar 

  • Davis M, Lleo S (2013a) Jump-diffusion risk-sensitive asset management II: jump-diffusion factor model. SIAM J Control Optim (forthcoming)

  • Davis M, Lleo S (2013b) Jump-diffusion risk-sensitive benchmarked asset management. In: Gassmann H, Ziemba W (eds) Stochastic programming: applications in finance, energy, planning and logistics, World, no 4 in World Scientific Series in Finance, pp 97–128

  • Davis M, Guo X, Wu G (2009) Impulse control of multi-dimensional jump diffusions. SIAM J Optim Control (to appear)

  • Fleming W, Rishel R (1975) Deterministic and stochastic optimal control. Springer, Berlin

    Book  Google Scholar 

  • Fleming W, Soner H (2006) Controlled Markov processes and viscosity solutions, stochastic modeling and applied probability, vol 25, 2nd edn. Springer, New York

    Google Scholar 

  • Ikeda N, Watanabe S (1981) Stochastic differential equations and diffusion processes. North-Holland Publishing Company, Amsterdam, New York

  • Kuroda K, Nagai H (2002) Risk-sensitive portfolio optimization on infinite time horizon. Stoch Stoch Re 73:309–331

    Article  Google Scholar 

  • Ladyzenskaja O, Solonnikov V, Uralceva O (1968) Linear and quasilinear equations of parabolic type. American Mathematical Society

  • Luenberger D (1969) Optimization by vector space methods. Wiley, New York

    Google Scholar 

  • Øksendal B, Sulem A (2005) Applied stochastic control of jump diffusions. Springer, Berlin, Heidelberg, New York

  • Pham H (1998) Optimal stopping of controlled jump diffusion processes: a viscosity solution approach. J Math Syst Estim Control 8(1):1–27

    Google Scholar 

  • Rudolf M, Ziemba WT (2004) Intertemporal surplus management. J Econ Dyn Control 28:975–990

    Article  Google Scholar 

  • Touzi N (2002) Stochastic control and application to finance. Special research Semester on Financial Mathematics, Scuola Normale Superiore, Pisa, April 29–July 15 2002. http://www.cmap.polytechnique.fr/~touzi/pise02

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Imperial College London, London, UK

    Mark H. A. Davis

  2. Finance Department and Behavioral Sciences Research Centre, NEOMA Business School, 59 rue Pierre Taittinger, 51100 , Reims, France

    Sébastien Lleo

Authors
  1. Mark H. A. Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sébastien Lleo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sébastien Lleo.

Additional information

We thank the participants to the XIII International Conference on Stochastic Programming (ICSP2013) for helpful suggestions and comments. Part of this paper was written while the second author was visiting at the Hausdorff Institute of Mathematics, University of Bonn, during the Trimester Program “Stochastic Dynamics in Economics and Finance”. The second author gratefully acknowledges support from Région Champagne Ardennes and the European Union through the RiskPerform Grant.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Davis, M.H.A., Lleo, S. Jump-diffusion asset–liability management via risk-sensitive control. OR Spectrum 37, 655–675 (2015). https://doi.org/10.1007/s00291-014-0371-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-014-0371-x

Keywords

Search

Navigation