Renewal theory with exponential and hyperbolic discounting

Probability in the Engineering and Informational Sciences

Volumn 22, Issue 1, 2008, Pages 53-74

  Van Der Weide, J A M ^a   Suyono, ^b   Van Noortwijk, J M ^a,c  

^a Delft University of Technology ^*  (Netherlands)

^b UNIVERSITAS NEGERI JAKARTA   (Indonesia)

^c HKV CONSULTANTS   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

HYPERBOLIC FUNCTIONS; LIFE CYCLE; RANDOM PROCESSES;

ASYMPTOTIC EXPANSION; DISCOUNTED COSTS; HYPERBOLIC DISCOUNTING; LIFECYCLE COSTS; MAINTENANCE DECISIONS; OPTIMAL INVESTMENTS; SECOND MOMENTS; TIME VALUE OF MONEY;

COSTS;

EID: 37349083519     PISSN: 02699648     EISSN: 14698951     Source Type: Journal    
DOI: 10.1017/S0269964808000041     Document Type: Article

References (26)

1. Atherton, E. & French, S. (1998). Valuing the future: A MADA example involving nuclear waste storage. Journal of Multi-Criteria Decision Analysis 7(6): 304-321.
2. Brealey, R.A. & Myers, S.C. (2003). Principles of corporate finance, 7th ed. New York: McGraw-Hill/Irwin.
3. Dall'Aglio, G. (1964). Present value of a renewal process. The Annals of Mathematical Statistics 35(3): 1326-1331.
4. den Iseger, P. (2006). Numerical transform inversion using Gaussian quadrature. Probability in the Engineering and Informational Sciences 20(2): 1-44.
5. Feller, W. (1949). Fluctuation theory of recurrent events. Transactions of the American Mathematical Society 67(1): 98-119.
6. Frederick, S., Loewenstein, G., & O'Donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature 40(2): 351-401.
7. Herrnstein, R.J. (1981). Self-control as response strength. In C.M. Bradshaw, E. Szabadi, & C.F. Lowe (eds.), Quantification of steady-state operant behavior. Amsterdam: Elsevier/North-Holland.
8. Léveillé, G. & Garrido, J. (2001). Moments of compound renewal sums with discounted claims. Insurance: Mathematics and Economics 28(2): 217-231.
9. Loewenstein, G. & Prelec, D. (1992). Anomalies in intertemporal choice: Evidence and an interpretation. Quarterly Journal of Economics 107(2): 573-597.
10. Mazur, J.E. (1987). An adjustment procedure for studying delayed reinforcement. In M.L. Commoms, J.E. Mazur, J.A. Nevin, & H. Rachlin (eds.), Quantitative analysis of behavior: The effect of delay and intervening events on reinforcement value. Hillsdale, NJ: Erlbaum, pp. 55-73.
11. Morey, R.C. (1966). Some stochastic properties of a compound-renewal damage model. Operations Research 14(5): 902-908.
12. Phelps, E.S. & Pollak, R.A. (1968). On second-best national saving and game-equilibrium growth. Review of Economic Studies 35(2): 185-199.
13. Rackwitz, R. (2000). Optimization: The basis of code-making and reliability verification. Structural Safety 22(1): 27-60.
14. Rackwitz, R. (2001). Optimizing systematically renewed structures. Reliability Engineering and System Safety 73(3): 269-279.
15. Rackwitz, R., Lentz, A., & Faber, M. (2005). Socio-economically sustainable civil engineering infrastructures by optimization. Structural Safety 27(3): 187-229.
16. Samuelson, P.A. (1937). A note on measurement of utility. Review of Economic Studies 4(2): 155-161.
17. Smith, W.L. (1954). Asymptotic renewal theorems. Proceedings of the Royal Society of Edinburgh, Section A (Mathematical and Physical Sciences) 64: 9-48.
18. Smith, W.L. (1958). Renewal theory and its ramifications. Journal of the Royal Statistical Society, Series B 20(2): 243-302.
19. Smith, W.L. (1966). On necessary and sufficient conditions for the convergence of the renewal density. Transactions of the American Mathematical Society 104(1): 79-100.
20. Tijms, H.C. (2003). A first course in stochastic models. New York: Wiley.
21. van Noortwijk, J.M. (2003). Explicit formulas for the variance of discounted life-cycle cost. Reliability Engineering and System Safety 80(2): 185-195.
22. Wagner, H.M. (1975). Principles of operations research, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall.
23. Washburn, A. (1992). Present values with renewals. Management Science 38(6): 846-850.
24. Weitzman, M.L. (1998). Why the far-distant future should be discounted at its lowest possible rate. Journal of Environmental Economics and Management 36(3): 201-208.
25. Weitzman, M.L. (2001). Gamma discounting. American Economic Review 91(1): 260-271.
26. Wolff, R.W. (1989). Stochastic modeling and the theory of queues. Englewood Cliffs, NJ: Prentice-Hall.