ON MEAN–VARIANCE HEDGING UNDER PARTIAL OBSERVATIONS AND TERMINAL WEALTH CONSTRAINTS

Vitalii Makogin (), Alexander Melnikov () and Yuliya Mishura ()
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Vitalii Makogin: Institute of Stochastics, Ulm University, D-89069, Ulm, Germany
Alexander Melnikov: Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB T6G 2G1., Canada
Yuliya Mishura: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, Kyiv, 01601, Ukraine

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 05, 1-21

Abstract: In this paper, a mean-square minimization problem under terminal wealth constraint with partial observations is studied. The problem is naturally connected to the mean–variance hedging (MVH) problem under incomplete information. A new approach to solving this problem is proposed. The paper provides a solution when the underlying pricing process is a square-integrable semi-martingale. The proposed method for study is based on the martingale representation. In special cases, the Clark–Ocone representation can be used to obtain explicit solutions. The results and the method are illustrated and supported by examples with two correlated geometric Brownian motions.

Keywords: Mean–variance hedging; partial information; observable and unobservable contingent claims; Clark–Ocone representation; semi-martingale approach; stochastic derivative; geometric Brownian motion (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024917500315

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