期刊文献+

有限期限上具有随机利率的最优投资消费模型 被引量:4

OPTIMAL INVESTMENT AND CONSUMPTION MODEL WITH STOCHASTIC INTEREST RATE ON A FINITE TIME HORIZON
原文传递
导出
摘要 文章考虑有限期限上的最优投资消费问题.风险资产服从几何布朗运动,利率服从一个遍历的Markov过程.目标是累积消费和终值财富贴现的幂效用期望最大化.利用动态规划原理推导出值函数所满足的HJB方程,并利用上下解方法证明了对应非线性抛物型偏微分方程终值问题解的存在唯一性,最后证明了验证性定理. In this paper, we consider an optimal investment and consumption problem on a finite time horizon. The price of risky asset obeys a geometric Brownian motion, and interest rate varies according to an ergodic Markov process. The goal is to choose optimal investment and consumption policies to maximize the expected discounted power utilities of the accumulative consumption and the terminal wealth. The HJB equation is derived using dynamic programming principle, and the existence and uniqueness of solution of the terminal value problem for the corresponding non- linear parabolic partial differential equation are obtained using the sub-supersolution method, finally, the verification theorem is obtained.
出处 《系统科学与数学》 CSCD 北大核心 2014年第8期914-924,共11页 Journal of Systems Science and Mathematical Sciences
基金 国家重点基础研究发展计划(973-2007CB814901)资助项目
关键词 随机利率 最优投资消费 HJB方程 上下解 幂效用. Stochastic interest rate, optimalequation, subsolution and supersolution, powerinvestment and consumption, HJButility.
  • 相关文献

参考文献14

  • 1Merton R C. Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics, 1969, 51(3): 247-257.
  • 2Merton R C. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 1971, 3: 373-413.
  • 3Fleming W H, Pang T. An application of stochastic control theory to financial economics. SIAM Journal on Control and Optimization, 2004, 43: 502-531.
  • 4Pang T. Portfolio optimization models on infinite time horizon. Journal of Optimization Theory and Applications, 2004, 22(3): 119-143.
  • 5Pang T. Stochastic portfolio optimization with log utility. International Journal of Theoretical and Applied Finance, 2006, 9(6): 869-887.
  • 6Noh E J, Kim J H. An optimal portfolio model with stochastic volatility and stochastic interest rate. Journal of Mathematical Analysis and Applications, 2011, 375: 510-522.
  • 7Korn R, Kraft H. A stochastic control approach to portfolio problems with stochastic interest rates. SIAM Journal on Control and Optimization, 2001, 40(4): 1250-1269.
  • 8Detemple J, Rindisbacher M. Closed-form solutions for optimal portfolio selection with stochastic interest rate and investment constraints. Mathematical Finance, 2005, 15(4): 539-568.
  • 9Li J Z, Wu R. Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility. Applied Stochastic Models in Business and Industry, 2009, 25: 407- 420.
  • 10Lioui A, Poncet P. On optimal portfolio choice under stochastic interest rates. Journal of Eco- nomic Dynamics and Control, 2001, 25: 1841-1865.

同被引文献48

  • 1王利峰,孟庆欣.随机利率下有违约风险的最优投资组合[J].复旦学报(自然科学版),2005,44(3):382-387. 被引量:8
  • 2王春峰,吴启权,李晗虹.资产配置中如何管理通货膨胀和随机利率风险:一种中长期投资问题[J].系统工程,2006,24(4):60-64. 被引量:8
  • 3哈维尔.微观银行学[M].成都:西南财经大学出版社,2000..
  • 4罗默.高级宏观经济学(第二版)[M].上海:上海财经大学出版社,2003..
  • 5MERTON R C.An intertemporal capital asset pricing model[J].Econometrica,1973,41(5):867-887.
  • 6COX J C,INGERSOLL J E,ROSS S A.A theory of the term structure of interest rates[J].Econometrica,1985,53(2):385-407.
  • 7WACHTER J.Risk aversion and allocate on to long term bonds[J].Journal of Economic Theory,2003,112(2):325-333.
  • 8SANGVINATSOS A,WACHTER J.Does the failure of the expectation hypothesis matter for long-term investors[J].Journal of Finance,2005,60(1):179-230.
  • 9LIU J.Portfolio selection in stochastic environments[J].Review of Financial Studies,2007,20(1):1-39.
  • 10CHANG H,RONG X M.An investment and consumption problem with CIR interest rate and stochastic volatility[J].Abstract and Applied Analysis,2013,doi:10.1155/2013/219397.

引证文献4

二级引证文献7

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部