Present value distributions with applications to ruin theory and stochastic equations

Stochastic Processes and their Applications

Volumn 71, Issue 1, 1997, Pages 123-144

  Gjessing, Håkon K ^a   Paulsen, Jostein ^b  

^a HAUKELAND UNIVERSITY HOSPITAL   (Norway)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

Characteristic function; Integro differential equation; Laplace transform; Present value distribution; Ruin probability; Stochastic equation

Indexed keywords

EID: 0031592036     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00072-0     Document Type: Article

References (18)

1. Bateman, H., 1954. Tables of Integral Transforms, vol. I. McGraw-Hill, New York.
2. Chamayou, J.F., Letac, G., 1991. Explicit stationary distributions for composition of random functions and products of random matrices. J. Theoret. Probab. 4, 3-36.
3. Dufresne, D., 1990. The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuarial J., 39-79.
4. Dufresne, D., 1996. On a property of gamma distributions. Bernoulli, 2, 287-291.
5. Feller, W., 1971. An Introduction to Probability Theory and its Applications, vol. II. Wiley, New York.
6. Fishman, G.S., 1996. Monte Carlo - Concepts, Algorithms, and Applications. Springer, New York.
7. Goldie, C.M., 1991. Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1, 126-166.
8. Harrison, J.M., 1977. Ruin problems with compounding assets. Stochast. Process. Appl. 5, 67-79.
9. Jensen, J.L., 1995. Saddlepoint Approximations. Oxford University Press, Oxford.
10. Lebedev, N.N., 1972. Special Functions and their Applications. Dover Publications, New York.
11. Liptser, R.S., Shiryayev, A.N., 1989. Theory of Martingales. Kluwer, Dordrecht.
12. Nilsen, T., Paulsen, J., 1996. On the distribution of a randomly discounted compound Poisson process. Stochast. Process. Appl. 61, 305-310.
13. Norberg, R., 1996. Ruin problems with assets and liabilities of diffusion type. Working Paper No. 137, Laboratory of Actuarial Mathematics, University of Copenhagen.
14. Paulsen, J., 1993. Risk theory in a stochastic economic environment. Stochast. Process. Appl. 46, 327-361.
15. Paulsen, J., 1997. Present value of some insurance portfolios. Scand. Actuarial J., 11-37.
16. Sundt, B., 1993. An Introduction to Non-Life Insurance Mathematics, 3rd. ed. Verlag Versicherungswirtschaft e.V.
17. Vervaat, W., 1979. On a stochastic difference equation and a representation of non-negative infinitely divisible random variables. Adv. Appl. Probab, 11, 750-783.
18. Yor, M., 1992. On some exponential functionals of Brownian motion. Adv. Appl. Probab. 24, 509-531.