Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model
Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model
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DOI：
10.1137/090760180
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发表时间：
2010-01
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通讯作者：
Mark H. A. Davis;Sébastien Lleo
中科院分区：
文献类型：
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作者：
Mark H. A. Davis;Sébastien Lleo
本文考虑了一个资产组合优化问题，其中资产价格由布朗运动和泊松随机测度驱动的随机微分方程表示，漂移是辅助扩散因子过程的函数。遵循Bielecki、普利斯卡、永井和其他人早期工作的标准是风险敏感优化（相当于在方差约束下最大化预期增长率）。利用黑田和永井引入的测度变换技术，我们证明了该问题归结为求解因子过程中的某个随机控制问题，该问题不存在跳。本文的主要结果是证明了风险敏感跳跃扩散问题可以完全用抛物型Hamilton-Jacobi-Bellman偏微分方程来刻画，并且该偏微分方程存在经典$（C^{1，2}）$解.
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai, and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance). By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of this paper is to show that the risk-sensitive jump-diffusion problem can be fully characterized in terms of a parabolic Hamilton-Jacobi-Bellman PDE rather than a partial integro-differential equation, and that this PDE admits a classical $(C^{1,2})$ solution.