资产定价，稳健投资与随机最优控制的动态规划

发布时间：2019-06-07 17:29

【摘要】：本文研究非对称信息下的资产定价,随机微分效用下的稳健投资与非Lipschitz条件下的随机最优控制动态规划理论,分为以下三个部分：第一部分讨论内部人交易问题。这一章是在Back(1992)和Cho(2003)关于内部投资者模型上的拓展。在这个金融市场中一共有三类人：内部投资者,不知情交易者和做市商。我们考虑一类比Cho(2003)研究的模型更广的一类定价规则。我们主要用动态规划的方法,证明了当内部人是风险中性时,虽然定价规则形式上依赖累计交易量的轨迹,但市场均衡时,定价规则中的“随机压力”消失,价格本质上还是仅依赖市场上累计交易量,而不依赖其轨迹。相应的,我们的结论推广了Back(1992)和Cho(2003)在经典模型中的结论。第二部分考虑具有随机微分效用函数的投资者在连续时间中跨期消费投资问题。我们建立了推广的随机微分效用函数的生成元f关于y具有单调性下的验证定理。作为应用,我们考虑了(a)稳健的消费投资组合和(b)推广的随机微分效用函数下的消费投资组合。在(a)中,我们给出了稳健的投资者的最优解,而且将他们的行为和普通的投资者进行了比较。在(b)中,我们也给出了推广的随机微分效用函数下投资者行为的刻画。第三部分我们讨论递归随机最优控制问题。我们研究描述随机微分效用的BSDE的生成元.f关于y是非Lipschitz的情况。我们给出了这类问题的动态规划原理,及在一定的条件下,证明值函数是对应HJB方程的粘性解。
[Abstract]:In this paper, the asset pricing under asymmetric information, robust investment under stochastic differential utility and stochastic optimal control dynamic programming under non-Lipschitz conditions are studied, which are divided into the following three parts: the first part discusses the problem of insider trading. This chapter is an extension of the internal investor model in Back (1992) and Cho (2003). There are three categories of people in this financial market: internal investors, uninformed traders and market makers. We consider a class of pricing rules which are more extensive than the model studied by Cho (2003). We mainly use the method of dynamic programming to prove that when the insiders are risk-neutral, although the pricing rules formally rely on the trajectory of cumulative trading volume, when the market is balanced, the "random pressure" in the pricing rules disappears. In essence, prices still rely only on cumulative trading volume in the market, rather than on their tracks. Accordingly, our results generalize the conclusions of Back (1992) and Cho (2003) in classical models. In the second part, the problem of cross-temporal consumer investment with stochastic differential utility function is considered. We establish the verification theorem of the generator f of the extended stochastic differential utility function with respect to y with monotonicity. As an application, we consider the (a) robust consumer portfolio and the (b) extended stochastic differential utility function. In (a), we give the optimal solution of robust investors, and compare their behavior with ordinary investors. In (b), we also give the characterization of investor behavior under the extended stochastic differential utility function. In the third part, we discuss the problem of recurrent stochastic optimal control. We study the generator of BSDE describing stochastic differential utility. F is a case where y is non-Lipschitz. In this paper, the dynamic programming principle of this kind of problem is given, and under certain conditions, it is proved that the value function is the viscous solution of the corresponding HJB equation.
【学位授予单位】：复旦大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：O221.3;F830

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