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A Stochastic Control Approach to Risk Management Under Restricted Information

Author

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  • Wolfgang J. Runggaldier
  • Anna Zaccaria

Abstract

We use techniques from discrete‐time stochastic control under partial state information to determine a shortfall‐risk minimizing investment strategy in the case when there is only restricted information on the underlying market model and transaction costs as well as shortselling constraints are present. The approach is adaptive in the sense that it takes into account all the information on the underlying model that becomes successively available to an economic agent by observing the prices in the market. As an immediate byproduct of the approach it is possible to determine the entire shortfall distribution corresponding to the optimal strategy and to various values of the initial capital.

Suggested Citation

  • Wolfgang J. Runggaldier & Anna Zaccaria, 2000. "A Stochastic Control Approach to Risk Management Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 277-288, April.
    • Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:277-288
    DOI: 10.1111/1467-9965.00094
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    Cited by:

    1. Barbara Trivellato, 2009. "Replication and shortfall risk in a binomial model with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 1-26, March.
    2. Gerard Awanou, 2007. "Shortfall risk minimization in a discrete regime switching model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 30(1), pages 71-78, May.
    3. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkiö, 2023. "Optional projection under equivalent local martingale measures," Finance and Stochastics, Springer, vol. 27(2), pages 435-465, April.
    4. Tak Siu & Howell Tong & Hailiang Yang, 2004. "On Bayesian Value at Risk: From Linear to Non-Linear Portfolios," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(2), pages 161-184, June.

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