Risk-minimizing hedging for stochastic payment styled contingent claims

Measuring financial risks with the conditional mean square error process of cost, we construct risk-minimizing hedging model and study the dynamic hedging problem for stochastic payment styled contingent claims. For any given contingent claim with stochastic payment flow, we firstly prove that there is a unique risk-minimizing hedging strategy by taking advantage of the G-K-W decomposition theorem; then, with the Bellman's principle of optimality, explicit expressions of hedging strategies are acquired and these expressions only comprise conditional moments of risky asset's price and stochastic payment; lastly, at the end of this paper, we take insurance payment for an example to illustrate the technique and conclusions mentioned in this paper are reasonable and feasible.