A Benchmark Approach to Risk-Minimization under Partial Information

TL;DR

This paper develops a framework for risk-minimizing hedging strategies in incomplete markets under partial information, using the benchmark approach and Galtchouk-Kunita-Watanabe decomposition, with applications to jump-diffusion models.

Contribution

It characterizes optimal hedging strategies under partial information using the benchmark approach and dual projections, extending classical methods to incomplete and partially observed markets.

Findings

Explicit characterization of optimal strategies under partial information

Application to Markovian jump-diffusion models with unobservable factors

Connection between partial and full information decompositions

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 num\'{e}raire 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.