The Relationship Between Two Kinds Of Stochastic Control Methods And Application In Finance

In this paper,the maximum principle and dynamic programming princi-ple are used to study the cash flow valuation problem with terminal limitation which satisfies a recursive utility function in financial market.First of all,it is assumed that there are only two kinds of risk and risk-free securities in the market.The utility function of the client satisfies the hyperbolic absolute risk aversion function(HARA).This problem is transformed into a random port-folio optimization problem for FBSDE by Lagrange multiplication method.Then,using the maximum principle and dynamic programming,the optimal strategy is obtained.At the same time,the optimal strategies calculated by the two methods coincidence.Subsequently,we gave the connection between the value function V,the generalized Hamiltonian function G,and adjoint processes p,q,k.Finally,we simulate and analyze the optimal strategy,using random simulations,through Matlab,analyzing the influence of each param-eter on the optimal strategy.