Risk-sensitive asset management on both finite and infinite time horizons are treated on a market with a bank account and a risky stock. The risk-free interest rate is formulated as a geometric Brownian motion, and affects the return of the risky stock. The problems become standard risk-sensitive control problems. We derive the Hamilton–Jacobi–Bellman equations and study these solutions. Using solutions, we construct optimal strategies and optimal values.

中文翻译：

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具有对数正态利率的风险敏感资产管理

在具有银行账户和风险股票的市场上处理有限和无限时间范围内的风险敏感资产管理。无风险利率被表述为几何布朗运动，并影响风险股票的回报。这些问题成为标准的风险敏感控制问题。我们推导出 Hamilton-Jacobi-Bellman 方程并研究这些解。使用解决方案，我们构建最优策略和最优值。