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The effect of the jumps in price and volatility on dynamic portfolio choice

机译：价格和波动率的跳跃对动态投资组合选择的影响

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Based on the double-jump diffusion model with the affine structure in the state variable, this paper applies stochastic control method to obtain the analytical solution of dynamic portfolio choice, which maximizes the expected power utility of portfolio terminal wealth, and studies the effect of jumps in security price and volatility on dynamic portfolio choice. Analysis shows that the state variables in portfolio model both have no “market timing” for power utility investor; the jumps in price and volatility make the dynamic portfolio problem to blend a standard dynamic problem with a static buy-and-hold problem; jumps in price make the investor not only never take a leverage or short position on the risky asset but also never invest all of his wealth on the risky asset in dynamic portfolio; the jumps result in positive or negative jump hedging demand, which depends on that the direction of jumps in price is upward or downward, at the same time, the jumps in volatility will in further enhance or weaken the magnitude of jump hedging demand. This study demonstrates that jumps in price and volatility change the standard dynamic portfolio problem in several important ways, and should be considered in the context of dynamic portfolio choice.
机译：基于状态变量中具有仿射结构的双跳扩散模型，本文采用随机控制方法获得动态投资组合选择的解析解，最大程度地提高了投资组合终端财富的预期效用，并研究了跳跃效应。证券价格和波动性的动态投资组合选择。分析表明，投资组合模型中的状态变量都没有针对电力公用事业投资者的“市场时机”。价格和波动率的跳跃使动态投资组合问题将标准动态问题与静态购买和持有问题混合在一起;价格的上涨使投资者不仅永远不会对风险资产采取杠杆作用或做空仓位，而且也永远不会将其全部财富投资于动态投资组合中的风险资产;跳跃会导致正面或负面的跳跃对冲需求，这取决于价格跳跃的方向是向上还是向下，同时，波动率的跳跃会进一步提高或减弱跳跃对冲需求的规模。这项研究表明，价格和波动率的跳跃会以几种重要方式改变标准的动态投资组合问题，应该在动态投资组合选择的背景下加以考虑。

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