Threshold-Type Policies for Real Options Using Regime-Switching Models

Bensoussan, Alain; Zhang, Yan; Yin, George

doi:10.1137/110833300

Cited by 21 publications

(24 citation statements)

References 14 publications

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“…Suppose that the follower makes an investment at time τ by paying cost K , and he will receive a perpetual cash flow

δ_{2} Y false(t false)

per unit time. This cash flow will depend on the condition at time τ; namely, the project value from the operation is the expected discounted cash flow stream given by

δ_{2} E [\int_{τ}^{\infty} e^{- μ false(s - τ false)} Y_{y} false(s false) d s | F_{τ}] = δ_{2} a_{z (τ)} Y false(τ false),

where

a_{i} false(μ + λ_{i} - α_{i} false) - λ_{i} a_{1 - i} = 1,

for

i = 0, 1

; see Bensoussan et al () for details.…”

Section: Follower's Problem and Optimal Policymentioning

confidence: 99%

“…From Bensoussan et al (), for each

i \in M

, there exists a unique

v_{i} false(y false) \in C^{1} false(0, \infty false)

and

v_{i}^{''} \in L^{\infty} false(0, \infty false)

, the solution of , satisfies

({, \begin{matrix} 0true - \frac{1}{2} y^{2} σ_{i}^{2} v_{i}^{''} - α_{i} y v_{i}^{'} + (λ_{i} + μ) v_{i} - λ_{i} v_{1 - i} + δ_{2} y - μ K = 0 0 < y < {\hat{y}}_{i}, \\ 0true v_{i} (0) = K, v_{i} (y) = 0 y \geq {\hat{y}}_{i}, \end{matrix})

with

{\hat{y}}_{i}

uniquely defined. Let

{\hat{τ}}_{y, i}

be the optimal stopping time of the follower which corresponds to the thresholds

\overset{y_{0}}{true}

and

\overset{y_{1}}{true}

, that is

{\overset{τ}{true}}_{y, i} = τ_{y, i} false(\overset{y_{0}}{true}, \overset{y_{1}}{true} false) .

Therefore, the follower will undertake the investment (i.e., enter into the market) when the cash flow exceeds a certain threshold level.…”

Section: Follower's Problem and Optimal Policymentioning

confidence: 99%

“…From Bensoussan et al (2012), for each i ∈ M, there exists a unique v i (y) ∈ C 1 (0, ∞) and v i ∈ L ∞ (0, ∞), the solution of (3.4), satisfies…”

Section: Follower's Problem and Optimal Policymentioning

confidence: 99%

“…It is therefore important to develop models that incorporate market cycles and the overall economic climate. Similar to Sotomayor and Cadenillas (2009) and Bensoussan, Yan, and Yin (2012), we incorporate a regime-switching model to capture market and economic effects.…”

Section: Introductionmentioning

confidence: 99%

“…First, our work explicitly formulates the leader's payoff function in Stackelberg competition under regime-switching uncertainty. We face technical complexities not present in either Bensoussan et al (2012) due to the lack of competition, or in Bensoussan et al (2010) because of the lack of regime changes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Real Options With Competition and Regime Switching

Bensoussan

Hoe

Zhang

et al. 2014

Mathematical Finance

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In this paper, we examine irreversible investment decisions in duopoly games with a variable economic climate. Integrating timing flexibility, competition, and changes in the economic environment in the form of a cash flow process with regime switching, the problem is formulated as a stopping-time game under Stackelberg leader-follower competition, in which both players determine their respective optimal market entry time. By extending the variational inequality approach, we solve for the free boundaries and obtain optimal investment strategies for each player. Despite the lack of regularity in the leader's obstacle and the cash flow regime uncertainty, the regime-dependent optimal policies for both the leader and the follower are obtained. In addition, we perform comprehensive numerical experiments to demonstrate the properties of solutions and to gain insights into the implications of regime switching.

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“…Suppose that the follower makes an investment at time τ by paying cost K , and he will receive a perpetual cash flow

δ_{2} Y false(t false)

per unit time. This cash flow will depend on the condition at time τ; namely, the project value from the operation is the expected discounted cash flow stream given by