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Risk-sensitive investment in a finite-factor model

Author

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  • Grzegorz Andruszkiewicz
  • Mark H. A. Davis
  • S'ebastien Lleo

Abstract

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner and Lipster (2014) is used to prove the martingale property of the relevant density processes.

Suggested Citation

  • Grzegorz Andruszkiewicz & Mark H. A. Davis & S'ebastien Lleo, 2014. "Risk-sensitive investment in a finite-factor model," Papers 1407.5278, arXiv.org, revised Jan 2016.
    • Handle: RePEc:arx:papers:1407.5278
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    References listed on IDEAS

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    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. Mark H. A. Davis & Sebastien Lleo, 2009. "Jump-Diffusion Risk-Sensitive Asset Management," Papers 0905.4740, arXiv.org, revised Mar 2010.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Grzegorz Andruszkiewicz & Mark Davis & Sébastien Lleo, 2013. "Taming animal spirits: risk management with behavioural factors," Annals of Finance, Springer, vol. 9(2), pages 145-166, May.
    5. Tomasz Bielecki & Daniel Hernández-Hernández & Stanley R. Pliska, 1999. "Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 167-188, October.
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    Cited by:

    1. Lijun Bo & Huafu Liao & Xiang Yu, 2017. "Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching," Papers 1712.05676, arXiv.org, revised Oct 2018.
    2. Jerome L Kreuser & Didier Sornette, 2017. "Super-Exponential RE Bubble Model with Efficient Crashes," Swiss Finance Institute Research Paper Series 17-33, Swiss Finance Institute.

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