Irreversible investment with random delay and partial prepayment

Chen, Pengzhan; Song, Yingda

doi:10.1016/j.orl.2022.06.005

Cited by 1 publication

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“…In quantitative finance, optimal stopping problems are formulated to study the pricing of American‐style options and the refinancing decision of a floating mortgage (refer to Fusai and Roncoroni (2008) for a detailed discussion of the problems). Additionally, a large body of literature exists in finance on irreversible investment problems, in which a firm solves an optimal stopping problem to determine the timing of investment in an irreversible project, where the revenue of the investment is modeled as a function of a Markov process (see, e.g., Bernanke, 1983; Dixit et al., 1994; Mcdonald & Siegel, 1987; Pindyck, 1991; Kogan, 2001; Guo et al., 2005; De Angelis et al., 2017; Chen & Song, 2022). Another example is the multi‐armed bandit (MAB) problem, in which one is allowed to work on a single project among several alternatives, and it is necessary to determine the optimal policy to allocate resources dynamically.…”

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confidence: 99%

A general approximation method for optimal stopping and random delay

Chen

Song

2023

Mathematical Finance

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This study examines the continuous‐time optimal stopping problem with an infinite horizon under Markov processes. Existing research focuses on finding explicit solutions under certain assumptions of the reward function or underlying process; however, these assumptions may either not be fulfilled or be difficult to validate in practice. We developed a continuous‐time Markov chain (CTMC) approximation method to find the optimal solution, which applies to general reward functions and underlying Markov processes. We demonstrated that our method can be used to solve the optimal stopping problem with a random delay, in which the delay could be either an independent random variable or a function of the underlying process. We established a theoretical upper bound for the approximation error to facilitate error control. Furthermore, we designed a two‐stage scheme to implement our method efficiently. The numerical results show that the proposed method is accurate and rapid under various model specifications.

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