Controlled diffusion models for optimal dividend pay-out. (English) Zbl 1065.91529


91B30 Risk theory, insurance (MSC2010)
Full Text: DOI


[1] Asmussen, S., Approximations for the probability of ruin within finite time, Scandinavian Actuarial Journal, 57 (1985) · Zbl 0568.62092
[2] Asmussen, S., Ruin Probabilities (1995), World Scientific: World Scientific Singapore, to appear
[3] Borch, K., The theory of risk, Journal of the Royal Statistical, Society B, 29, 432-452 (1967) · Zbl 0153.49301
[4] Borch, K., The capital structure of a firm, Swedish Journal of Economics, 71, 1-13 (1969)
[5] Bowers, N. L.; Gerber, H. U.; Hickman, J. C.; Jones, D. A.; Nesbitt, C. J., Actuarial Mathematics (1986), The Society of Actuaries: The Society of Actuaries Itasca, IL · Zbl 0634.62107
[6] Bühlmann, H., Mathematical Methods in Risk Theory (1970), Springer: Springer Berlin · Zbl 0209.23302
[7] Buzzi, R., Optimale Dividendstrategien für den Risikoprozess mit austauschbaren Zuwächsen, (Ph.D. Dissertation 5388 (1974), ETH Zürich)
[8] Davis, M., Markov Models and Optimization (1993), Chapman and Hall: Chapman and Hall London · Zbl 0780.60002
[9] Dellacherie, C.; Meyer, P.-A., Probabilities et Potentiel. Theorie des Martingales (1980), Hermann: Hermann Paris
[10] de Finetti, B., Su un’impostazione alternativa dell teoria colletiva del rischio, (Transactions of the 15th International Congress of Actuaries, 2 (1957)), 433-443, New York
[11] Emanuel, D. C.; Harrison, J. M.; Taylor, A. J., A diffusion approximation for the ruin probability with compounding assets, Scandinavian Actuarial Journal, 37-45 (1975)
[12] Fleming, W. H.; Rishel, R. W., Deterministic and Stochastic Optimal Control (1975), Springer: Springer Berlin · Zbl 0323.49001
[13] Fleming, W. H.; Soner, M., Controlled Markov Processes and Viscosity Solutions (1993), Springer: Springer Berlin · Zbl 0773.60070
[14] Gerber, H. U., Games of economic survival with discrete- and continuous-income processes, Operations Research, 20, 37-45 (1972) · Zbl 0236.90079
[15] Gerber, H. U., On optimal cancellation of policies, ASTIN Bull., IX, 125-138 (1977)
[16] Gerber, H. U., An Introduction to Mathematical Risk Theory (1979), S.S. Huebner Foundation Monographs, University of Pennsylvania · Zbl 0431.62066
[17] Grandell, J., A class of approximations of ruin probabilities, Scandinavian Actuarial Journal, Suppliment, 37-52 (1977) · Zbl 0384.60057
[18] Grandell, J., A remark on ‘A class of approximations of ruin probabilities’, Scandinavian Actuarial Journal, 77-78 (1978) · Zbl 0389.62082
[19] Grandell, J., Aspects of Risk Theory (1990), Springer: Springer Berlin
[20] Harrison, J. M., Ruin problems with compounding assets, Stochastic Processess and their Application, 5, 67-79 (1977) · Zbl 0361.60053
[21] Harrison, J. M., Brownian Motion and Stochastic Flow Systems (1985), Wiley: Wiley New York · Zbl 0659.60112
[22] Harrison, J. M.; Taksar, M. I., Instantaneous control of Brownian motion, Mathematics of Operations Research, 8, 439-453 (1983) · Zbl 0523.93068
[23] Iglehart, D. L., Diffusion approximations in collective risk theory, Journal of Applied Probability, 6, 285-292 (1969) · Zbl 0191.51202
[24] Karatzas, I.; Shreve, S. E., Connections between optimal stopping and singular stochastic control. I. Monotone follower problem, SIAM Journal Control Optimization, 22, 856-877 (1984) · Zbl 0551.93078
[25] Karlin, S.; Taylor, H. M., A Second Course in Stochastic Processes (1981), Academic Press: Academic Press New York · Zbl 0469.60001
[26] Martin-Löf, A., A method for finding the optimal decision rule for a policy holder of an insurance with a bonus system, Scandinavian Actuarial Journal, 23-29 (1973) · Zbl 0322.62102
[27] Martin-Löf, A., Premium control in an insurance system, an approach using linear control theory, Scandinavian Actuarial Journal, 1-27 (1983) · Zbl 0509.62097
[28] Martin-Löf, A., Lectures on the use of control theory in insurance, Scandinavian Actuarial Journal, 1-25 (1994) · Zbl 0802.62090
[29] Møller, C. M., Point processes and martingales in risk theory, (Ph.D. thesis (1994), Laboratory of Insurance Mathematics, University of Copenhagen)
[30] Schmidli, H., A General Insurance Risk Model, (Ph.D. thesis, 9881 (1992), ETH Zürich) · Zbl 0876.60072
[31] Schmidli, H., Diffusion approximations for a risk process with the possibility of borrowing and interest, Stochastic Models, 10, 365-388 (1993) · Zbl 0793.60095
[32] Seal, H. L., The Stochastic Theory of a Risk Business (1969), Wiley: Wiley New York · Zbl 0196.23501
[33] Seal, H. L., Survival Probabilities (1978), Wiley: Wiley New York · Zbl 0386.62088
[34] Whittle, P., (Optimization over Time. — Dynamic Programming and Stochastic Control, Vol II (1983), Wiley: Wiley New York) · Zbl 0503.92020
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