Multi-asset option pricing based on stochastic optimal control assuming correlations lie in given intervals

The assumption of constant correlation between the underlyings cannot be satisfied in market. In this paper, we find the multi-asset option price intervals assuming the correlation lies within a given interval. First we transform this financial problem to a stochastic optimal control problem, then obtain options' maximum and minimum price models through dynamic programming principle. We further discuss how to solve the Black-Scholes-Barenblatt equation through finite difference schemes. We conclude this paper by giving its applications in multi asset option market, comparing with the analytical solutions, and giving a method how to identify arbitrage opportunity in multi-asset option markets.