Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model
Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model
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DOI：
10.1137/110825881
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发表时间：
2011-02
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影响因子：
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通讯作者：
Mark H. A. Davis;Sébastien Lleo
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文献类型：
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作者：
Mark H. A. Davis;Sébastien Lleo
在本文中，我们扩展了先前在一个因子模型中的跳跃扩散风险敏感资产管理问题的研究[SIAM J. Financial Math]。[j], 2(2011)，第22—54页]通过允许因素过程和资产价格的跳跃，以及随机波动和投资约束。在这种情况下，Hamilton- Jacobi- Bellman （HJB）方程是一个偏积分微分方程（PIDE）。我们能够证明，找到这个PDE的粘度解等价于找到一个相关PDE的粘度解，经典结果给出唯一性。在此基础上，一个策略改进论证和抛物型偏微分方程的经典结果表明，HJB偏微分方程存在唯一的光滑解。最优投资策略是由最小化哈密顿函数的反馈控制给出的。
In this article we extend our earlier work on the jump-diffusion risk-sensitive asset management problem in a factor model [SIAM J. Financial Math., 2 (2011), pp. 22--54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the Hamilton--Jacobi--Bellman (HJB) equation is a partial integro-differential equation (PIDE). We are able to show that finding a viscosity solution to this PIDE is equivalent to finding a viscosity solution to a related PDE, for which classical results give uniqueness. With this in hand, a policy improvement argument and classical results on parabolic PDEs show that the HJB PIDE admits a unique smooth solution. The optimal investment strategy is given by the feedback control that minimizes the Hamiltonian function appearing in the HJB PIDE.