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arXiv · 1307.6036

A Benchmark Approach to Risk-Minimization under Partial Information

Claudia Ceci·Katia Colaneri·Alessandra Cretarola
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Abstract

In this paper we study a risk-minimizing hedging problem for a semimartingale incomplete financial market where d+1 assets are traded continuously and whose price is expressed in units of the numéraire portfolio. According to the so-called benchmark approach, we investigate the (benchmarked) risk-minimizing strategy in the case where there are restrictions on the available information. More precisely, we characterize the optimal strategy as the integrand appearing in the Galtchouk-Kunita-Watanabe decomposition of the benchmarked claim under partial information and provide its description in terms of the integrands in the classical Galtchouk-Kunita-Watanabe decomposition under full information via dual predictable projections. Finally, we apply the results in the case of a Markovian jump-diffusion driven market model where the assets prices dynamics depend on a stochastic factor which is not observable by investors.

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Claudia Ceci, Katia Colaneri, Alessandra Cretarola. 2013-07-23. A Benchmark Approach to Risk-Minimization under Partial Information. https://doi.org/10.1016/j.insmatheco.2014.01.003

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