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Mean‐Variance Hedging and Forward‐Backward Stochastic Differential Filtering Equations

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  • Guangchen Wang
  • Zhen Wu

Abstract

This paper is concerned with a mean‐variance hedging problem with partial information, where the initial endowment of an agent may be a decision and the contingent claim is a random variable. This problem is explicitly solved by studying a linear‐quadratic optimal control problem with non‐Markov control systems and partial information. Then, we use the result as well as filtering to solve some examples in stochastic control and finance. Also, we establish backward and forward-backward stochastic differential filtering equations which are different from the classical filtering theory introduced by Liptser and Shiryayev (1977), Xiong (2008), and so forth.

Suggested Citation

  • Guangchen Wang & Zhen Wu, 2011. "Mean‐Variance Hedging and Forward‐Backward Stochastic Differential Filtering Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:310910
    DOI: 10.1155/2011/310910
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
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