Study On The Assets Mix Strategies Under Continuous-time Framework

Investments and consumptions of an individual and assets managements of an institute are very important activities. The portfolios theory of Markowitz becomes helpless while faces the large amount uncertainties in the reality. In our thesis, we take account of the most common constrains on investments, consumptions and assets allocations. By adopting singular stochastic control technique, we solve problems on continuous-time, intertemporal Investments and consumptions under friction market, assets allocation with stochastic interest rate and inflation and pensions under stochastic environments. The analytic forms are achieved in most of the above problems. The assets mix strategies under continuous-time framework in this thesis are scheduled by the following:1. It supposes that asset prices evolve through time according to Ito diffusion processes, the expected yield and variance are impacted by exogenous states variables. We studies dynamic strategies of maximizing the utility of Consumption and Investment and minimizing risk. The multi-objective models are established and the solutions are given.2. We consider the optimal Consumption and Investment Strategy for a hyperbolic absolute risk aversion (HARA) investor who faces proportional transaction costs and maximizes expected utility of finite/ infinite horizon with only two-asset. Using the concavity and the homothetic property of the value function, the HJB can be reduced from a PDE to an ODE. The analytic forms of the value functions in the transaction regions are achieved and HJB equation. We also introduce the option pricing technique under transaction cost.3. The advices of popular investment advisors are apparently inconsistent with the Separation Theorem; it is the so-called Canner Puzzle. A bank account, nominal bonds, and stocks can be traded. We provide the optimal asset allocation strategy with interest rate risk and inflation risk, which can be seen as a background risk. Uncertainty about future interest rates is represented by the Hull&White two-factor model .The solutions are given and the economic significations are analyzed by theoretic and illustrative calculations. The rational explications of the diversities between the popular investment advices and the Separation Theorem are given.4. We study defined-contribution plans by maximizing the terminal expected wealth under a general framework. In an economics environment with stochastic investment opportunities, a fund manager is faced with market risks and backgroundrisks, which is represented with the salary risk. We first construct the mathematical model, then guess the value function and its parameters forms, and finally, we achieve the optimal strategy and the solution. We also make presentations on this strategy.5. A Generalized Wiener Process can simulate the price process of a financial asset. But actually, the asset's price changes non-continuous. We introduce a Poisson Process to simulate the"jump"stochastic process model. We first construct the model, and then introduce the financial market and the dynamics budget equation. We discuss the two problems that the asset price evolves with Poisson Process and the risk factor evolves with Poisson Process. The optimal allocation strategies are given for these two problems.