Dynamic Asset Allocation With Event Risk

Major events often cause abrupt changes in stock prices and volatility, which follow the jump diffusion process, then domestic and foreign scholars devote to study dynamic asset allocation problem in jump diffusion environment. On the basis of the predecessors, we probe into the effect of stock price jump, volatility jump, inflation, consumption and exchange rate factors on the dynamic asset allocation strategy in this article, where stock prices and volatility are subject to jump diffusion process.First, this thesis studies dynamic asset allocation problem with event risk under the inflation. Through deducing the dynamics of the asset price discounted by inflation, a stochastic optimal control model for dynamic asset allocation with inflation is established under the event-risk framework. By using the dynamic programming principle, we achieve approximate analytical solutions to the optimal portfolio problem. The influence of the inflation volatility, asset price jump size and return volatility jump size on an investor’s optimal asset allocation strategy in simplified model is analyzed by the MATLAB. Then this paper show that investors with event risk will reduce positions of risky assets, regardless of how the asset price jump direction and size change; However, for a particular asset prices jump size risk lover will increase positions of risk asset with the addition of volatility jump size; When the volatility of inflation is too high, investors will hold very little risk assets, who are less sensitive to volatility jumped size and stock price changes.Second, this thesis discusses the optimal consumption and portfolio problem with event risk. We establish a model about optimal consumption and portfolio choice with HARA utility under the event-risk framework. By using the dynamic programming principle, we obtain approximate analytical solutions to the optimal consumption and portfolio problem. Through numerical simulation, we analyze the effect of the jump size on an investor’s optimal consumption and portfolio. We find that investors with event risk will often increase their consumption and reduce the holdings of risky assets, but for the specific size of the risk asset prices jump, investors will reduce their consumption and increase the positions of risk assets with the addition of volatility jump size.Finally, this thesis investigates asset allocation for a international investor with event risk. We deduce the dynamic of the risk asset price denoted by the local currency with Ito-Doeblin formula. Then, the optimal asset allocation strategy is achieved by the method of stochastic control for the investor with the power utility to maximizing the expected utility of his (her) terminal wealth. We analyze the effect of exchange rate and return volatility jump on optimal international portfolio by numerical simulation. The study indicates that foreign will continue to increase positions of risk assets with the rise of spot exchange rate expectations, but when the spot expected rate exceeds a certain value, the foreign investors will steadily hold some one. For a specific asset prices jump size, the foreign with volatility jump will increase properly positions of their risk assets for expected return.