An Optimal Multiple Stopping Approach to Infrastructure Investment Decisions

Dahlgren, Eric; Leung, Tim

doi:10.2139/ssrn.2216025

Cited by 12 publications

(19 citation statements)

References 29 publications

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“…We now compare the linear threshold scheduling policies (obtained from Algorithm 1) with two existing schemes: Table 2 BIC model order selection for the popular live session. The maximum likelihood estimated parameters are given in (24). The BIC criteria was run for S varying from 2 − 12 (only values for 2 − 6 are shown below).…”

Section: Multiple Ad Scheduling: Performance Resultsmentioning

confidence: 99%

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Multiple stopping time POMDPs: Structural results & application in interactive advertising on social media

2018

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This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal multiple stopping policy. The main results are as follows: i) The optimal multiple stopping policy is shown to be characterized by threshold curves Γ l , for l = 1, · · · , L, in the unit simplex of Bayesian Posteriors. ii) The stopping sets S l (defined by the threshold curves Γ l ) are shown to exhibit the following nested structure S l−1 ⊂ S l . iii) The optimal cumulative reward is shown to be monotone with respect to the copositive ordering of the transition matrix. iv) A stochastic gradient algorithm is provided for estimating linear threshold policies by exploiting the structural results. These linear threshold policies approximate the threshold curves Γ l , and share the monotone structure of the optimal multiple stopping policy. As an illustrative example, we apply the multiple stopping framework to interactively schedule advertisements in live online social media. It is shown that advertisement scheduling using multiple stopping performs significantly better than currently used methods.

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Section: Multiple Ad Scheduling: Performance Resultsmentioning

confidence: 99%

“…Also, the user interest in online social media typically evolves slowly [29]. 9 The transition matrices computed on real dataset in Section 5 follow a tridiagonal structure; refer to (24). 10 The following continuous distribution satisfy (A2): Exponential, Normal, Gamma, Weibull, Lognormal, Beta.…”

Section: Discussion Of Assumptionsmentioning

confidence: 99%

Multiple stopping time POMDPs: Structural results & application in interactive advertising on social media

2018

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“…Having derived the optimal production schedule and total firm value, we then split the firm value into two components: equity and debt. We view the equity as a call option on the firm's assets (Merton, 1974), and thus, determine the optimal investment timing for the associated real option (McDonald and Siegel, 1986;Dixit, 1994;Dahlgren and Leung, 2015). We extend the real options literature by not only showing that gold miner equities behave like options on gold, but also demonstrating how the resulting stochastic implied leverage evolves with respect to spot gold.…”

Section: Related Studiesmentioning

confidence: 86%

How to mine gold without digging

2019

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This paper examines the main drivers of the returns of gold miner stocks and ETFs during 2006–2017. We solve a combined optimal control and stopping problem to demonstrate that gold miner equities behave like real options on gold. Inspired by our proposed model, we construct a method to dynamically replicate gold miner stocks using two factors: the spot gold ETF and market equity portfolio. Furthermore, through each firm’s factor loadings on the replicating portfolio, we dynamically infer the firm’s implied leverage parameters of our model using the Kalman Filter. We find that our approach can explain a significant portion of the drivers of firm implied gold leverage. We posit that gold miner companies hold additional real options which help mitigate firm downside volatility, but these real options contribute to lower returns relative to the replicating portfolio when gold returns are positive.

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“…Such a valuation was made in Dahlgren and Leung (2013), where the value of consecutive investments, as a function of lifetime and lead time, was treated as an optimal multiple stopping problem. The main finding in that study was that increasing lifetime does not greatly increase the value of an investment scenario where multiple consecutive investments can be made.…”

Section: Investment Flexibilitymentioning

confidence: 99%