随机利率下美式几何平均亚洲期权的定价:一种随机最优控制方法

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
M. T. V. Martínez-Palacios, A. Hernández-del-Valle, Ambrosio Ortiz-Ramírez
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引用次数: 0

摘要

本文通过连续时间的随机最优控制,建立了消费和投资的最优决策模型,该模型由一个理性的经济主体,代表一个经济体,他是一个消费者和一个对风险不利的投资者;这是在随机长度的有限时间范围内。模型的假设是:一个HARA型的消费函数,一个具有随机生产过程的代表性公司,代理人投资一只股票和一份浮动执行权等于该股票认购的几何平均的美式亚洲看跌期权,均采用受控马尔可夫过程建模;以及银行账户本金的投资。用连续时间动态规划方法求解了该模型,得到了Hamilton-Jacobi-Bellman PDE,并提出了一个可分离变量函数作为设定消费和投资最优轨迹的解。在解分析中确定:在均衡状态下,短期利率的过程是由一个回归均值的平方根过程驱动的;通过一个风险溢价的微分方程系统,PDE被推断为相当于Black-Scholes-Merton,但对美式亚洲看跌期权进行估值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the pricing of Asian options with geometric average of American type with stochastic interest rate: A stochastic optimal control approach
In this work, through stochastic optimal control in continuous time the optimal decision making in consumption and investment is modeled by a rational economic agent, representative of an economy, who is a consumer and an investor adverse to risk; this in a finite time horizon of stochastic length. The assumptions of the model are: a consumption function of HARA type, a representative company that has a stochastic production process, the agent invests in a stock and an American-style Asian put option with floating strike equal to the geometric average subscribed on the stock, both modeled by controlled Markovian processes; as well as the investment of a principal in a bank account. The model is solved with dynamic programming in continuous time, particularly the Hamilton-Jacobi-Bellman PDE is obtained, and a function in separable variables is proposed as a solution to set the optimal trajectories of consumption and investment. In the solution analysis is determined: in equilibrium, the process of short interest rate that is driven by a square root process with reversion to the mean; and through a system of differential equations of risk premiums, a PDE is deduced equivalent to the Black-Scholes-Merton but to value an American-style Asian put option.
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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