Quadratic hedging for asset derivatives with discrete stochastic dividends

In this paper we analyze the effect of discrete stochastic dividends on the pricing and hedging of contingent claims, formulating the No Arbitrage condition without requiring the continuity of the implied gain process. We allow the stock jump dependence on an additional random source, still preserving the positivity of the stock value at the ex-dividend date. We characterize all the equivalent martingale measures and analyze the quadratic hedging approaches, as local risk minimizing and mean variance hedging.