Real Options With Competition and Regime Switching

Bensoussan, Alain; Hoe, SingRu; Zhang, Yan; Yin, George

doi:10.1111/mafi.12085

Cited by 19 publications

(5 citation statements)

References 30 publications

(38 reference statements)

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“…Comprehensive treatment and survey of the progress in switching diffusions can be found in [40,59]; see also [10,43,61,62] and references therein. For recent development and applications, we refer to [44,60] for related numerical methods for solutions of differential equations with switching, [50,51,52,53,55] for numerical methods for control and game problems, [5,21,22,24,25,54] and references therein for various applications in real options, insurance, mean-field models, and mathematical biology, among others. A recent paper written in a handbook style, providing the formulation and basic numerical methods of Markov chain approximation method is in [20].…”

Section: Formulation and Notationmentioning

confidence: 99%

A survey of numerical solutions for stochastic control problems: Some recent progress

Jin¹,

Qiu²,

Tran³

et al. 2022

NACO

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<p style='text-indent:20px;'>This paper presents a survey on some of the recent progress on numerical solutions for controlled switching diffusions. We begin by recalling the basics of switching diffusions and controlled switching diffusions. We then present regular controls and singular controls. The main objective of this paper is to provide a survey on some recent advances on Markov chain approximation methods for solving stochastic control problems numerically. A number of applications in insurance, mathematical biology, epidemiology, and economics are presented. Several numerical examples are provided for demonstration.</p>

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Section: Formulation and Notationmentioning

confidence: 99%

A survey of numerical solutions for stochastic control problems: Some recent progress

Jin¹,

Qiu²,

Tran³

et al. 2022

NACO

Self Cite

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“…Two players in a Stackelberg game use regime switching to determine their respective optimal market entry and establish their irreversible investments. They integrate timing flexibility, competition, and changes in the market environment that further translate in cash flows represented by operational profits (Bensoussan et al, 2017). Liu and Zhao (2013) studies options with two underlying assets whose prices are governed by the regime-switching geometric Brownian motion, where a lattice is constructed with a jump step size for the two variables.…”

Section: Lattice and Regime Switchingmentioning

confidence: 99%

Real options valuation with duopoly game-theoretic approach and regime switching

Diaz¹

2022

Preprint

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<p>New product demand continuously fluctuates through the life of the product. As a result, markets usually experience high volatility due to fluctuating demand. Hence, organizations must rapidly adapt and be flexible with such volatility. Management decisions cannot rely on traditional models that assume economic variables to be constant over time. Therefore, companies must advance and implement adequate strategies in resource allocation that help them survive in uncertain markets, and mitigate the associated risk from market uncertainty. This research aims to investigate product introduction strategies where two micro-economic theories can be applied: game-theoretic approach and a real options valuation. Specifically, a real options valuation framework with a flexible capacity that can be used to calculate the Net Present Value (NPV) and the optimal initial capacity to invest in a product, which is being introduced in a duopoly environment, is proposed. This framework is based on game theory applied to a duopoly market. A stochastic product life cycle characterized by a regime-switching approach and the consideration of two different game-theoretic models for the cases where competitors have perfect or imperfect information in the market are the main focal points of our study. Subsequently, different numerical examples comparing the results of NPV and optimal initial capacities from both game-theoretic models are presented. It is observed that the leader in the model with perfect information has an important advantage over its opponent because this company makes the first move to establish quantity to supply. Also, the leader in perfect information game has an advantage over the game with imperfect information since decisions with imperfect information have to be made simultaneously, and players need to balance all possible outcomes when making a choice. Consequently, in both models, one of the competitors obtains its maximum NPV when the other invests in the lowest level of capacity. Lastly, expansion and contraction costs play a critical role in the strategy of resource allocation as these costs are involved in capacity flexibility. Therefore, firms can adjust their production when product demand varies to maximize profits.</p>

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“…With the aid of the Feynman-Kac formulas, we may proceed to treat many stochastic control problems. For example, combining real options, game theory, and a regime-switching formulation with jumps, we may consider an irreversible investment problem with Stackelberg leader-follower competition and market regime changes (see the related work using switching diffusion formulation [4]). The treatment of the real options and the related problems with competition have received resurgent attention lately.…”

Section: Further Remarksmentioning

confidence: 99%

Feynman–Kac formulas for regime-switching jump diffusions and their applications

2015

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This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a general Lévy process and the switching part depends on the jump diffusion processes. Under broad conditions, the connections of such stochastic processes and the corresponding partial integro-differential equations are established. Related initial, terminal, and boundary value problems are also treated. Moreover, based on weak convergence of probability measures, it is demonstrated that a sequence of random variables related to the regime-switching jump diffusion process converges in distribution to the arcsine law.

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Real Options With Competition and Regime Switching

Cited by 19 publications

References 30 publications

A survey of numerical solutions for stochastic control problems: Some recent progress

A survey of numerical solutions for stochastic control problems: Some recent progress

Real options valuation with duopoly game-theoretic approach and regime switching

Feynman–Kac formulas for regime-switching jump diffusions and their applications

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