PhD Public Lecture (DSAS) - Junhe Chen
"Application of Stochastic Control to Portfolio Optimization and Energy Finance"
In this thesis, we study two continuous-time optimal control problems. The first describes competition in the energy market and the second aims at robust portfolio decisions for commodity markets. Both problems are approached via solutions of Hamilton-Jacobi-Bellman (HJB) and HJB-Isaacs (HJBI) equations.
In the energy market problem, our target is to maximize profits from trading crude oil by determining optimal crude oil production. We determine the optimal crude oil production rate by constructing a differential game between two types of players: a single finite-reserve producer and multiple infinite-reserve producers. We extend the deterministic unbounded-production model and stochastic monopolistic game to bounded-production and construct an $N$-player stochastic game using analytical and numerical solutions to the corresponding HJB equation. In this way, we compute the optimal strategies of oil production for four stylized players. As an example, applying the game-theory model above, we construct a deterministic and a stochastic differential-game model between four countries, and compare the real production and the forecast production in order to test the accuracy of the model.
In the robust portfolio optimization problem, we assume the investor allocates funds among a bond, a bank account, and a commodity that either pays a mean-reverting convenience yield, or follows an exponential Ornstein-Uhlenbeck (OU) process. In our settings, the interest rate of the bond follows a Vasicek model. We optimize the expected utility of terminal wealth, solving the corresponding HJBI equation via an exponential affine ansatz, which can be used to generate an optimal portfolio strategy. As part of our study, we fit our model to prices of crude oil, gold, copper and interest rates, leading to a meaningful empirical analysis. We concluded from the suboptimal analysis that the mis-specification of parameters and incompleteness of market lead to severe wealth-equivalent losses.
