Knightian Uncertainty, k-Ignorance, and Optimal Timing

We investigate within a continuous time setting how Knightian uncertainty characterized by k-ignorance affects the optimal timing policies of a risk-neutral and uncertainty averse investor in the case where the exercise payoff is monotonic. We prove that increased Knightian uncertainty unambiguously decreases the value of the optimal timing policy of an uncertainty averse investor. We also show that higher Knightian uncertainty accelerates timing by shrinking the continuation region whenever the termination payoff is independent of Knightian uncertainty. If this independence condition is not fulfilled, then our results indicate that higher Knightian uncertainty may decelerate optimal timing.Knightian uncertainty, k-ambiguity, optimal stopping, diffusions

Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective

We consider the valuation and optimal exercise policy of a δ- penalty minimum guaranteed payment option in the case where the value of the underlying dividend-paying asset follows a linear diffusion. We characterize both the value and optimal exercise policy of the considered game option explicitly and demonstrate that increased volatility increases the value of the option and postpones exercise by expanding the continuation region where exercising is suboptimal. An interesting and natural implication of this finding is that the value of the embedded cancellation rights of the issuer increase as volatility increases.minimum guaranteed payment, δ-penalty options, Dynkin games, linear diffusions

Irreversible Investment under Interest Rate Variability: New Results

The current extensive literature on irreversible investment decisions makes the assumption of constant interest rate. In this paper we study the impact of interest rate and revenue variability on the decision to carry out an irreversible investment project. Given the generality of the considered valuation problem, we first provide a thorough mathematical characterization of the problem and develop some new results. Contrary to what previous literature has suggested we establish that interest rate variability may have a profound decelerating or accelerating impact on investment demand depending on whether the current interest rate is below or above the long run steady state interest rate. Moreover, and importantly, allowing for interest rate uncertainty is shown to decelerate rational investment demand by raising both the required exercise premium of the irreversible investment opportunity and the value of waiting. Finally, we demonstrate that increased revenue volatility strengthens the negative impact of interest rate uncertainty and vice versa.irreversible investment, variable interest rates, free boundary problems.

Progressive Taxation and Irreversible Investment under Uncertainty

We analyze the impact of progressive taxation on irreversible investment under uncertainty. We show that if tax exemption is lower than sunk cost, higher tax rate will decelerate optimal investment by increasing the optimal investment threshold, while if tax exemption exceeds sunk cost, three different regimes arise. For "small" volatilities the optimal investment threshold is a positive function of volatility, but independent of tax rate. For "medium" volatilities it is independent of both tax rate and volatility. Finally, for "high" volatilities the optimal investment threshold depends positively on volatility, but negatively on tax rate so that we have "tax paradox".irreversible investments under uncertainty, progressive taxation

A General Approach to the Stochastic Rotation Problem with Amenity Valuation

This paper presents a new approach to study the optimal rotation policy with amenity valuation under uncertainty. We first postulate the stochastic forest value and assume plausibly that monetary value of amenities is a continuous and non-negative function of forest value thus presenting the trade-off between timber revenues and amenity values. Second, instead of using a dynamic programming approach, we derive a recursive representation of the total forest value and solve the optimal rotation threshold by applying ordinary non-linear programming techniques. Third, we characterize under certain set of conditions how the properties of both the expected cumulative value and the expected marginal cumulative value, accrued from amenity services, depend on the precise nature of the monetary valuation of amenities and what is the impact of volatility on these concepts. Finally, we illustrate our results explicitly in models based on logistic growth by focusing on the role of amenity valuation and volatility of forest value in the determination of Wicksellian and Faustmannian thresholds. Our theoretical and numerical findings emphasize the crucial importance of the nature of amenity valuation for the impact of higher volatility of forest value on the rotation thresholds.amenity valuation, optimal Faustmannian and Wicksellian rotation policy, stochatic impulse control

Wicksellian Theory of Forest Rotation under Interest Rate Variability

The current literature on optimal forest rotation makes the assumption of constant interest rate. However, the irreversible harvesting decisions of forest stands are typically subject to relatively long time horizons over which interest rates do fluctuate considerably. In this paper we apply the Wicksellian single rotation framework to extend the existing studies to cover the unexplored case of variable interest rate. Given the technical generality of the considered valuation problem, we provide a thorough mathematical characterization of the optimal timing problem and develop new results. We show that even in the deterministic case if the current interest rate deviates from its long-run steady state, interest rate variability changes the rotation age significantly when compared with the constant discounting case. Further, and importantly, allowing for interest rate uncertainty is shown to increase the optimal rotation period when the value of the optimal policy is a convex function of the current interest rate. In line with this finding, we also establish that increased interest rate volatility has a positive impact on the optimal rotation period.Wicksellian rotation, variable interest rates, linear diffusions, optimal stopping, free boundary problems