The Optimal Strategy With Dynamic Monetary Utility

First,based on Delbane's representation theorem of minimal penalty function,we defined our time consistent dynamic utility functionSecond,we consider the problem of utility maximization in incomplete market.Precisely speaking,we want to get the optimal strategy both in market with full uncertainty and market with partial uncertainty.Here,we use the measure set to show the uncertainty of financial marketsTo solve the problem,we make use of the tool of backward stochastic differential equations(BSDE in short)under a Brownian Motion filtration,and prove that the dynamic utility satisfies a BSDE,and compute the optimal strategy in two kinds of markets.Moreover,we prove that when the market is approaching to market with full uncertainty,the associate optimal strategy converges to the one in market with full uncertaintyLast,we consider the general case when penalty function is super quadratic...