TY - BOOK

T1 - Dynamic portfolio optimization with stochastic investment opportunities

AU - Zhang, Yumo

PY - 2023

Y1 - 2023

N2 - This thesis is comprised of nine independent research projects pertaining primarily to dynamic portfolio optimization with time-varying investment opportunities, model ambiguity, and relative performance concerns. We start with the optimal mean-variance portfolio selection problem with a 3/2 stochastic volatility in a complete market setting, where we derive, in closed form, both the static and dynamic optimality using a backward stochastic differential equation approach. Then, in incomplete market settings, we study more complicated cases within the framework of the mean-variance criteria under a hybrid model of stochastic volatility and stochastic interest rates, the family of state-of-the-art 4/2 stochastic volatility models with derivatives trading and uncontrollable random liabilities, and in the presence of mispricing, respectively. Next, three portfolio optimization problems under the expected utility maximization paradigm are investigated, where we consider the presence of stochastic volatility and affine short rates, stochastic income and stochastic inflation, and random liabilities under the hyperbolic absolute risk aversion preferences, respectively. The last two projects revolve around optimal asset-liability management problems with stochastic volatility in the non-Markovian cases, demonstrating the impact of model ambiguity and relative performance concerns on the behavior of the optimal investment strategies by means of the backward stochastic differential equations, in which the former one is modeled as a zero-sum stochastic differential game between the manager and the adverse market whereas the latter one is described by a non-zero-sum stochastic differential game between two competitive managers.

AB - This thesis is comprised of nine independent research projects pertaining primarily to dynamic portfolio optimization with time-varying investment opportunities, model ambiguity, and relative performance concerns. We start with the optimal mean-variance portfolio selection problem with a 3/2 stochastic volatility in a complete market setting, where we derive, in closed form, both the static and dynamic optimality using a backward stochastic differential equation approach. Then, in incomplete market settings, we study more complicated cases within the framework of the mean-variance criteria under a hybrid model of stochastic volatility and stochastic interest rates, the family of state-of-the-art 4/2 stochastic volatility models with derivatives trading and uncontrollable random liabilities, and in the presence of mispricing, respectively. Next, three portfolio optimization problems under the expected utility maximization paradigm are investigated, where we consider the presence of stochastic volatility and affine short rates, stochastic income and stochastic inflation, and random liabilities under the hyperbolic absolute risk aversion preferences, respectively. The last two projects revolve around optimal asset-liability management problems with stochastic volatility in the non-Markovian cases, demonstrating the impact of model ambiguity and relative performance concerns on the behavior of the optimal investment strategies by means of the backward stochastic differential equations, in which the former one is modeled as a zero-sum stochastic differential game between the manager and the adverse market whereas the latter one is described by a non-zero-sum stochastic differential game between two competitive managers.

M3 - Ph.D. thesis

BT - Dynamic portfolio optimization with stochastic investment opportunities

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -