Multi-period Principal-agent Portfolio Optimization Model

With the institutionalization of investors,more and more financial wealth is not managed directly by savers,but through a financial intermediary,and investment is predominantly delegated investment.In this model,an individual investor who is known as a principal entrusts the funds to professional fund manager who works as an agent.The agent optimizes the investment through portfolio optimization.In this case,two hot issues are designing the cost contract and optimizing the investments.Based on the principle-agent theory,portfolio optimization models for single-period have been built.In this thesis,an extended multi-period mean-variance portfolio optimization model is proposed by requiring a linear cost contract.The situations with or without risk-free asset will make a difference while constructing models.Hence,the optimal multi-period portfolio strategies and corresponding multi-period contracts between the principal and the agent are discussed under both situations.For the case with risk-free assets,the analytic expression of the optimal portfolio and its optimal contract are obtained by constructing an auxiliary function based on the dynamic programming principle.For the case that the risk-free asset is not included,an equation that the cost parameters are required to meet are presented,and optimal portfolio strategy for risky assets are provided to agents.In the simulation,two portfolio strategies are compared.One is the equal investment strategy,the other is the proposed delegate investment strategy which requires agency fees.The simulation results shows that,when investors own small amount of money,the equivalent investment strategy always dominates the other.And the delegate investment strategy dominates the equivalent one when they own a relatively large amount of money.Note that the existence of risk-free asset will not change the results.However,the expected utility of investors’ terminal wealth under the situation with risk-free asset is always better than that under the situation without risk-free asset,no matter what the strategy is.