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Ruin problems with compounding assets. (English) Zbl 0361.60053

MSC:
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60H05 Stochastic integrals
60J99 Markov processes
91A12 Cooperative games
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[1] Bartle, R.G., Elements of real analysis, (1964), Wiley New York · Zbl 0116.32302
[2] Beekman, J.A., Two stochastic processes, (1974), Halsted Press New York · Zbl 0275.60050
[3] Billingsley, P., Convergence of probability measures, (1968), Wiley New York · Zbl 0172.21201
[4] Bohman, H., Risk theory and Wiener processes, Astin bulletin, 7, 96-99, (1972)
[5] Breiman, L., Probability, (1968), Addison-Wesley Reading, MA · Zbl 0174.48801
[6] Cramér, H., Collective risk theory: A survey of the theory from the point of view of the theory of stochastic processes, ()
[7] Davidson, A., On the ruin problem in the collective theory of risk under the assumption of variable safety loading, Skand. aktuar. tidskrf. suppl., 70-83, (1969) · Zbl 0223.62117
[8] Emanuel, D.C.; Harrison, J.M.; Taylor, A.J., A diffusion approximation for the ruin function of a risk process with compounding assets, Scand. actuarial J., 58, 240-247, (1975) · Zbl 0322.62101
[9] Feller, W., An introduction to probability theory and its applications, Volume II, (1966), Wiley New York · Zbl 0138.10207
[10] Gerber, H., The discounted central limit theorem and its Berry-Esseen analogue, Ann. math. stat., 42, 389-392, (1971) · Zbl 0224.60012
[11] Gerber, H., Games of economic survival with discrete and continuous-income processes, Ops. rsch., 20, 37-45, (1972) · Zbl 0236.90079
[12] Gikhman, I.I.; Skorohod, A.V., Introduction to the theory of random processes, (1969), Saunders Philadelphia
[13] Gnedenko, B.V., Theory of probability, (1962), Chelsea, New York
[14] Grandell, J., A remark on Wiener process approximation of risk processes, Astin bulletin, 7, 100-101, (1972)
[15] Hunt, G.A., Some theorems concerning Brownian motion, Trans. amer. math. soc., 81, 294-319, (1956) · Zbl 0070.36601
[16] Iglehart, D.L., Diffusion approximations in collective risk theory, J. appl. prob., 6, 285-292, (1969) · Zbl 0191.51202
[17] Jung, J., A note on a classical result in the collective risk theory, Skand. aktuar. tidskr., 61, (1973), 000-000
[18] Mayer, P.A., Probability and potentials, (1966), Blaisdell Waltham, MA
[19] Philipson, C.; Philipson, C., A review of the collective theory of risk, parts I and II, Skand. aktuar. tidskr., Skand. aktuar. tidskr., 51, 117-133, (1968)
[20] Segerdahl, C.-O., Über einige risikotheoretische fragestellungen, Skand. aktuar. tidskr., 25, 43-83, (1942) · Zbl 0026.41901
[21] Segerdahl, C.-O., A survey of results in the collective theory of risk, (), 276-299 · Zbl 0122.15501
[22] Skorohod, A.V., Studies in the theory of random processes, (1965), Addison-Wesley Reading, MA
[23] Whitt, W., Stochastic abelian and Tauberian theorems, Z. wahr. verw. geb., 22, 251-267, (1972) · Zbl 0242.60005
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