Optimal hedging by the Martingale method in complete and incomplete markets

This paper applies the Martingale method proposed by Cox and Huang to find optimal wealth and optimal hedging strategies in the Black-Scholes-Vasicek economy. It starts with a review of the general solution of optimal wealth by the Martingale method, and then apply it to a power utility function. We investigate optimal hedging under three benchmark scenarios including a cash, a stock, and an inflation-indexed bond benchmark. We analyse optimal portfolio choices when inflation-indexed bonds are traded in complete markets and not traded in incomplete markets. The outcomes suggest that optimal wealth and hedging highly depend on the volatilities of benchmarks and the degree of risk aversion of investors.