Premium evaluation for different loss distributions using utility theory

Harman Preet Singh Kapoor; Kanchan Jain

Discussiones Mathematicae Probability and Statistics (2011)

  • Volume: 31, Issue: 1-2, page 41-58
  • ISSN: 1509-9423

Abstract

top
For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ( P m a x ) that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine P m a x by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr. The theoretical expressions have been derived and the results have also been depicted graphically for some values of distribution parameters.

How to cite

top

Harman Preet Singh Kapoor, and Kanchan Jain. "Premium evaluation for different loss distributions using utility theory." Discussiones Mathematicae Probability and Statistics 31.1-2 (2011): 41-58. <http://eudml.org/doc/277077>.

@article{HarmanPreetSinghKapoor2011,
abstract = {For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ($P_\{max\})$ that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine $P_\{max\}$ by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr. The theoretical expressions have been derived and the results have also been depicted graphically for some values of distribution parameters.},
author = {Harman Preet Singh Kapoor, Kanchan Jain},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {utility function; insurance},
language = {eng},
number = {1-2},
pages = {41-58},
title = {Premium evaluation for different loss distributions using utility theory},
url = {http://eudml.org/doc/277077},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Harman Preet Singh Kapoor
AU - Kanchan Jain
TI - Premium evaluation for different loss distributions using utility theory
JO - Discussiones Mathematicae Probability and Statistics
PY - 2011
VL - 31
IS - 1-2
SP - 41
EP - 58
AB - For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ($P_{max})$ that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine $P_{max}$ by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr. The theoretical expressions have been derived and the results have also been depicted graphically for some values of distribution parameters.
LA - eng
KW - utility function; insurance
UR - http://eudml.org/doc/277077
ER -

References

top
  1. [1] K.J. Arrow, The theory of risk aversion, Reprinted in: Essays in the Theory of Risk Bearing (Markham Publ. Co., Chicago, 90109, 1971). 
  2. [2] K. Borch, The Mathematical Theory of Insurance (D.C. Heath and Co., Lexington, MA, 1974). Zbl0363.90065
  3. [3] K. Borch, Economics of Insurance (North-Holland, Amsterdam, 1990). 
  4. [4] N.L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones and C.J. Nesbitt, Actuarial Mathematics (Society of Actuaries, 1997). 
  5. [5] D.C.M. Dickson, Insurance Risk and Ruin, International Series on Actuarial Science (Cambridge University Press, 2005). 
  6. [6] M.J. Goovaerts, F. De Vijlder and J. Haezendonck, Insurance Premium: Theory And Application (North-Holland, Amsterdam, 1984). 
  7. [7] L. Haim, Stochastic Dominance: Investment Decision Making under Uncertainty (Springer, 2006). Zbl1109.91037
  8. [8] C. Huang and R.H. Litzenberger, Foundations for Financial Economics (Prentice Hall, Englewood Cliffs, NJ, 1988). Zbl0677.90001
  9. [9] R. Kaas, M. Goovaerts, J. Dhaene and M. Denuit, Modern Actuarial Risk Theory (Kluwer Academic Publishers, 2004). Zbl1086.91035
  10. [10] R. Kaas, M. Goovaerts, J. Dhaene and M. Denuit, Actuarial Theory For Dependent Risks: Measure, Orders And Models, Vol. 10 (John Wiley, 2005). 
  11. [11] J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behaviour (Princeton University Press, 1944). Zbl0063.05930
  12. [12] H.H. Panjer, (ed.) Financial Economics, with Applications to Investments, Insurance and Pensions. Actuarial Foundation (Schaumburg, IL, 1998). 
  13. [13] J.W. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964) 122-136. Zbl0132.13906
  14. [14] U. Schmidt, Axiomatic Utility Theory under Risk, Lecture Notes in Economics and Mathematical Systems, 461 (Springer-Verlag, Berlin, 1998). 
  15. [15] C.L. Trowbridge, Fundamental Concepts of Actuarial Sciences. Actuarial Education and Research Fund (Itasca, IL, 1989). 
  16. [16] S. Wang, Insurance pricing and increased limits ratemaking by proportional hazard transforms, Insurance: Mathematics and Economics 17 (1995) 43-54. Zbl0837.62088
  17. [17] S. Wang, Premium calculation by transforming the Layer premium density, ASTIN Bulletin 26 (1996) 71-92. 
  18. [18] S. Wang and V.R. Young, Ordering risks: utility theory versus Yaari's dual theory of risk. IIPR Research Report 97-08 (University of Waterloo, Waterloo, 1997). Zbl0907.90102
  19. [19] D. Zwillinger and S. Kokoska, CRC Standard Probability and Statistics Tables and Formulae (Chapman and Hall, 2000). Zbl0943.62124

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.