Essays on risk management

This thesis consists of three parts. The first part studies the optimal portfolio selection of expected utility maximizing investors who must also manage their market-risk exposures. The risk is measured by a so-called weighted Value-at-Risk (WVaR) risk measure, which is a generalization of both Value-at-Risk (VaR) and Expected Shortfall (ES). The feasibility, well-posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. The second part analyses the impact of ES-based market-risk regulation on portfolio choice and asset prices. We study the optimal, dynamic portfolio and wealth/consumption policies of expected utility maximizing investors who must also manage market-risk exposure which is measured by Expected Shortfall (ES). We find that ES managers can incur larger losses when losses occur, compared to both VaR and benchmark managers. A general-equilibrium analysis reveals that the presence of ES managers increases the market volatility during periods of significant financial market stress, in both pure-exchange and production economies. The third part studies the optimal dynamic reinsurance policy for an insurance company whose surplus is modeled by the diffusion approximation of the classical Cram\'{e}r-Lundberg model. We assume the reinsurance premium is calculated according to the Mean-CVaR premium principle which generalizes Denneberg's absolute deviation principle and expected value principle. Moreover, we require that both the ceded loss and retention functions are non-decreasing to rule out the moral hazard. Under the objective of minimizing the ruin probability, we obtain the optimal reinsurance policy explicitly, which is more complicated than the contracts widely studied in the dynamic reinsurance literature.