Dynamic Planning Of Asset Pricing, Steady Investment And Stochastic Optimal Control

The thesis is concerned with microstructure of asset prices, robust investment with a stochastic differential utility and the relevant stochastic dynamic program-ming for optimal stochastic controls.Part1studies the insider trading model of Back (1992) and Cho (2003), where the market consists of an insider, noise traders and competitive market makers who set price. We investigate a larger class of price processes than what Cho (2003) has considered. By dynamic programming, we show that when the insider is risk-neutral, the price still only depends on the cumulative market order. As a corollary, this part extends the equilibrium result of Back (1992) and Cho (2003).Part2examines a continuous time intertemporal consumption and portfolio choice problem for an investor with a recursive preference of Epstein-Zin type. We provide a generalized verification theorem under a weaker non-Lipschitz condition than Kraft et al.(2011). As two applications, we consider the following two problem-s:(a) the investor worries about model misspecification and seeks a robust decision rule,(b) the investor with a generalized stochastic differential utility (GSDU) seek-s the optimal consumption and portfolio. Under (a), we formulate HJB equation of the robust investor and provide explicit solutions. We also compare our robust solutions with non-robust ones. Under (b), we characterize those investors.Part3is concerned with recursive control problem. When the aggregator f is monotonic in y. we give the corresponding dynamic programming principle for the optimal control. Under suitable conditions, we show that the value function is the viscosity solution to the corresponding Hamilton-Jacobi-Bellman equation.