Continuous-Time Delegated Portfolio Management Problem With Drift And Stochastic Volatility Control

Delegating investment decisions to portfolio managers is an important issue in practice and has attracted the interest of researchers over decades.Securities investment fund is an important form of delegated portfolio management.The principal-agent relationship in security investment fund is distinctive,in which the risk of output is endogenous,i.e.,the risk is selected by fund managers.While the study of optimal contract in classical principal-agent setup has been extensively studied,relatively few have been studied in the context of delegated portfolio management in finance.Continuous-time principal-agent models have developed rapidly with applications to expanding areas of financial research.It is well known from the existing literature that the volatility of the cash-flow importantly affects both risk-sharing and incentives in contracting.This dissertation studies the contracting problem between an individual investor and a professional portfolio manager in a continuous-time principal-agent framework.There are following two parts about my studies in the paper:First,we study a continuous-time principal-agent problem where the risk-neutral agent can privately and meaningfully choose the drift and volatility of a cash flow,while the risk-averse principal only continuously observes the managed cash flows over time.The optimal action of fund managers in the model is randomly simulated with the method of Monte Carlo.The results illustrate that the optimal contract consists of four parts: the reservation utility determined in the labor market,the cost of effort,the compensation risk imposed on the agents in order to give him incentives to work,and the risk premium to be paid to the agents for the imposed compensation risk.The optimal effort and volatility control are given by a system of binary equations.Specially,if the logarithm function of the volatility control is a component of the funds' drift term,the agents should maintain the stability of the total fluctuation while controlling the fluctuation.Second,in view of the special form of remuneration for private equity fund,adelegated portfolio management model with the control of drift and volatility based on the risk aversion of agents is built from the perspective of the fund managers.In addition,the problems of optimal investment scale and sharing proportion of privately offered funds are studied.The results demonstrate that whether it is the increase of management fees or the improvement of asset management performance,the agents all hope to increase the asset management scale.The higher the asset management rate,the smaller the sharing proportion.The agents' optimal volatility control will decrease with the increase of the asset management scale.The optimal investment scale increases with the increase of asset management scale,and gradually becomes stable.