Application of Stochastic Optimal Control in Finance

Asset allocation theory and practice has been applied to many problems of institutional investors. In this dissertation, we consider the following two problems: Abstract i) Optimal portfolio and spending rules for endowment funds. Abstract ii) Capital adequacy management for banks in the Lévy market. Abstract Part I: We investigate the role of different spending rules in a dynamic asset allocation model for an endowment fund. In particular, we derive the optimal portfolios under the consumption-wealth ratio rule (CW strategy) and the hybrid rule (hybrid strategy) and compare them with a theoretically optimal (Merton's) strategy for both spending and portfolio allocation. Furthermore, we show that the optimal portfolio is less risky with habit as compared with the optimal portfolio without habit. Similarly, the optimal portfolio under hybrid strategy is less risky than both CW and Merton's strategy for given set of constant parameters. Thus, endowments following hybrid spending rule use asset allocation to protect spending. Our calibrated numerical analysis on US data shows that the consumption under hybrid strategy is less volatile as compared to other strategies. However, hybrid strategy comparatively outperforms the conventional Merton's strategy and CW strategy when the market is highly volatile but under-performs them when there is a low volatility. Overall, the hybrid strategy is effective in terms of stability of spending and intergenerational equity because, even if it allows fluctuation in spending in the short run, it guarantees the convergence of spending towards its long term mean. Abstract Part II: We investigate the capital adequacy management and asset allocation problems for a bank whose risk process follows a jump-diffusion process. Capital adequacy management problem is based on regulations in Basel III Capital Accord such as the capital adequacy ratio (CAR) which is calculated by the dividing the bank capital by total risk-weighted assets (TRWAs). Capital adequacy management requires a bank to reserve a certain amount for liquidity. We derive the optimal investment portfolio for a bank with constant absolute risk aversion (CARA) preferences and then the capital adequacy ratio process of the bank is derived, conditional on the optimal policy chosen.