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The Markov Chain Market

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  • Norberg, Ragnar

Abstract

We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differential equations. An excursion into risk minimization in the incomplete case illustrates the matrix techniques that are instrumental in the model.

Suggested Citation

  • Norberg, Ragnar, 2003. "The Markov Chain Market," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 265-287, November.
    • Handle: RePEc:cup:astinb:v:33:y:2003:i:02:p:265-287_01
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    Citations

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    Cited by:

    1. Jamaal Ahmad & Mogens Bladt, 2022. "Phase-type representations of stochastic interest rates with applications to life insurance," Papers 2207.11292, arXiv.org, revised Nov 2022.
    2. Nicole Bäuerle & Ulrich Rieder, 2009. "MDP algorithms for portfolio optimization problems in pure jump markets," Finance and Stochastics, Springer, vol. 13(4), pages 591-611, September.
    3. Kraft, Holger & Steffensen, Mogens, 2009. "Asset allocation with contagion and explicit bankruptcy procedures," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 147-167, January.
    4. Norberg, Ragnar, 2006. "Dynamic greeks," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 123-133, August.
    5. Cheung, Ka Chun & Yang, Hailiang, 2005. "Optimal stopping behavior of equity-linked investment products with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 599-614, December.
    6. Ragnar Norberg, 2005. "Interest Guarantees in Banking," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 351-370.
    7. Marcus C. Christiansen, 2021. "Time-dynamic evaluations under non-monotone information generated by marked point processes," Finance and Stochastics, Springer, vol. 25(3), pages 563-596, July.
    8. Qing Zhang, 2013. "When to sell a Markov chain asset?," Papers 1309.7507, arXiv.org.
    9. Ragnar Norberg, 2013. "Optimal hedging of demographic risk in life insurance," Finance and Stochastics, Springer, vol. 17(1), pages 197-222, January.
    10. Huiling Wu, 2013. "Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 918-934, September.

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