ON HYPERBOLIC TIME DISCOUNTING IN EXHAUSTIBLE RESOURCE MODELS: AN APPLICATION TO WORLD OIL RESOURCES

ABSTRACT. Recent research on discounting in long term economic models involves hyperbolic discounting, in which the marginal discount rate shrinks as time passes. To investigate hyperbolic discounting and exhaustible resource allocation, this work develops a discrete‐time world oil model and model solution procedure, then uses the model to examine the consequences of adopting conventional (constant annual) discounting when hyperbolic discounting is appropriate, of adopting one hyperbolic discount rate path when a different hyperbolic path is appropriate, and of adopting hyperbolic discounting when conventional discounting is appropriate. Five conventional and two hyperbolic discount rate paths are considered. One hyperbolic path is that used by Nordhaus and Boyer [2000]; the other is that recommended by Weitzman [2001]. The generality of the findings is also assessed.     

Corrigendum to “Belief functions contextual discounting and canonical decompositions” [International Journal of Approximate Reasoning 53 (2012) 146–158]

Proposition 4 and Theorem 1 of the article “Belief functions contextual discounting and canonical decompositions” [International Journal of Approximate Reasoning 53 (2012) 146–158] provide an erroneous result. We give here the true result with a correct proof.     

Corrigendum to “A note on the Loewenstein–Prelec theory of intertemporal choice” [Math. Social Sci. 52 (1) (2006) 99–108]

In a critique of the Loewenstein and Prelec [Loewenstein G., Prelec D., 1992. Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics 107, 573–597] theory of intertemporal choice, [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] point out four errors. One of the alleged errors was that the elasticity of the value function in prospect theory is decreasing. But it is in fact increasing. We provide a correction and a formal proof. As a corollary, we show that the elasticity of the value function is bounded between zero and one. Nevertheless, all the remaining points in [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] remain valid     

Infinite horizon stopping problems with (nearly) total reward criteria

We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε$\epsilon$-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump–diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.     

On dividend strategies with non-exponential discounting

In this paper, we study the dividend maximization problem with a non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to Markov strategies. This is a time inconsistent control problem. The equilibrium HJB-equation is given and the verification theorem is proven for a general discount function. Considering a mixture of exponential discount functions and a pseudo-exponential discount function, we get equilibrium dividend strategies and the corresponding equilibrium value functions by solving the equilibrium HJB-equations.     

Non-exponentiality in electron transfer kinetics: Static versus dynamic disorder models

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation—in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element,V _el.     

具随机折现的博弈期权定价问题

对具随机折现的博弈期权定价问题进行了研究,在满足一个可积性条件的情况下,借用过份函数等工具给出了期权价格的表达式和买卖双方的最优停止策略.对于不满足可积性条件的情况,推广了相关文献的结果,并给出了τ＊存在的条件.最后给出了一个例子.     

Limit of the solutions for the finite horizon problems as the optimal solution to the infinite horizon optimization problems

In this paper, we consider how to construct the optimal solutions for the undiscounted discrete time infinite horizon optimization problems. We present the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problem under two modified overtaking criteria, as well as the conditions under which it is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of a simple one-sector growth model to examine the impacts of discounting on the optimal path.     

Asset Pricing Using Finite State Markov Chain Stochastic Discount Functions

This article fuses two pieces of theory to make a tractable model for asset pricing. The first is the theory of asset pricing using a stochastic discounting function (SDF). This will be reviewed. The second is to model uncertainty in an economy using a Markov chain. Using the semi-martingale dynamics for the chain these models can be calibrated and asset valuations derived. Interest rate models, stock price models, futures pricing, exchange rates can all be introduced endogenously in this framework.     

Conditions for the existence of decision horizons for discounted problems in a stochastic environment: A note

In this note, we extend the sufficiency conditions obtained by Bean and Smith for the existence of decision and forecast horizons in discounted deterministic problems to a stochastic environment. Also developed are some examples for illustration of the results and the need for the development of necessary and sufficient conditions for undiscounted problems.