具有切换收益的几何布朗运动极大值的折现最优停止问题

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Advances in Applied Probability Pub Date : 2021-03-01 DOI:10.1017/apr.2020.57

P. Gapeev, P. Kort, M. Lavrutich

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引用次数: 7

摘要

摘要根据具有两个状态的连续时间马尔可夫链的动力学，我们给出了具有收益切换的几何布朗运动的运行最大值的一些折扣最优停止问题的闭式解。证明是基于将原始问题简化为等效自由边界问题，并通过光滑拟合和正反射条件求解后一个问题。我们证明了最优停止边界被确定为一阶非线性常微分方程的相关二维系统的最大解。所获得的结果与Black–Merton–Scholes模型中具有固定和浮动沉没成本的实际切换回溯期权的估值有关。

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Discounted Optimal Stopping Problems for Maxima of Geometric Brownian Motions With Switching Payoffs

Abstract We present closed-form solutions to some discounted optimal stopping problems for the running maximum of a geometric Brownian motion with payoffs switching according to the dynamics of a continuous-time Markov chain with two states. The proof is based on the reduction of the original problems to the equivalent free-boundary problems and the solution of the latter problems by means of the smooth-fit and normal-reflection conditions. We show that the optimal stopping boundaries are determined as the maximal solutions of the associated two-dimensional systems of first-order nonlinear ordinary differential equations. The obtained results are related to the valuation of real switching lookback options with fixed and floating sunk costs in the Black–Merton–Scholes model.

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来源期刊

Advances in Applied Probability 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Advances in Applied Probability has been published by the Applied Probability Trust for over four decades, and is a companion publication to the Journal of Applied Probability. It contains mathematical and scientific papers of interest to applied probabilists, with emphasis on applications in a broad spectrum of disciplines, including the biosciences, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.