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Two Stochastic Control Problems In Capital Structure and Portfolio Choice

This thesis mainly focuses on two problems in capital structure and individual's life-cycle portfolio choice. In the first problem, we derive a stochastic control model to optimize banks' dividend and recapitalization policies and calibrate that to a sample of U.S. banks in the situation where we model banks' true accounting asset values as partially observed variables due to the opaqueness in banks' assets. By the calibrated model, the noise in reported accounting asset values hides about one-third of the true asset return volatility and raises the banks' market equity value by 7.8\% because the noise hides the banks' solvency risk from banking regulators. Particularly, those banks with a high level of loan loss provisions, nonperforming assets, and real estate loans, and with a low volatility of reported total assets have noisy accounting asset values. Because of the substantial shock on the true asset values, the banks' assets were more opaque during the recent financial crisis. In the second problem, we present an optimal portfolio selection model with voluntary retirement option in an economic situation, where an investor is facing borrowing and short sale constraints, as well as the cointegration between the stock and labor markets. Our model reinterprets the non-participation puzzle in stock investment and early retirement in market booms. Investor's willingness to retire earlier becomes stronger as risk aversion increases or as wages decline in the long term. Consistent with the empirical evidence, we find that retirement flexibility makes the optimal portfolio invest less in the stock market. We also find that our model-generated portfolio share rises in wealth.

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