incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion … technique for the underlying volatility process, we derive explicit expression for the solution of the FBSDE up to the third … order of volatility-of-volatility, which can be directly translated into the optimal investment strategy. We compare our …

stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density … not model a foreign exchange rate's variance such as in Heston[1993], but its volatility that follows a general time … exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to …