The Readout of Merton's Problem on Infinite horizon - Stochastic Optimal Control Modelling

The optimization problem of a portfolio mainly consists in describing the investment choices of an individual whose degree of risk aversion is known, described by the utility function. The Merton problem is the first continuous time optimal investment model that assumes a market with N risky and a risk-free asset. We consider a portfolio in which, given an initial wealth, it is no longer possible to deposit or withdraw money, and whose dynamics are therefore linked only to fluctuations in the value of the assets that compose it. In classical methods for solving these problems, the main attempts are focused to determine the solution by introducing the value function via dynamic programming and Hamilton-Jacobi-Bellman equation. In this article, it is introduced a hybrid method to solve stochastic optimal control problems (SOCPs) to find of an appropriate optimal trajectory and control. This new approach is combined of multi-step stochastic differential transform method and approximation solution method of infinite horizon context via finite horizon. An applicable example in management science is also presented to show the ability and efficiency of the new method especially in comparison.

کلیدواژه ها:

Stochastic Modelling ، dynamic programming ، Optimal Control Problems ، Optimization Merton’s Portfolio Problem