Risk Management in Finance and Insurance via Stochastic Optimization.
详细信息
文摘
This thesis is concerned with the study of the risk-constrained portfolio selection problem arising from an ordinary investor and the insurer being an investor. We first consider the problem for an insurer who can invest her surplus into financial market. With value at risk VaR) imposed as the dynamic risk constraint, the portfolio selection problem is considered with two objectives: the ruin probability minimization and wealth utility maximization. A closed-form solution is found by solving the associated Hamilton-Jacob-Bellman HJB) equation for the first problem. By using the exponential utility function, we solve the second problem by transforming this stochastic optimal control problem into a deterministic optimal control one and using control parameterization method. Second, we consider the risk-constrained utility maximizing problem with a jump diffusion model and a regime switching model for an ordinary investor. Conditional value at risk CVaR) and maximal value at risk MVaR) are used as the risk constraint in the two models, respectively. The associated HJB equations are treated with numerical techniques.