Home  Current  Past volumes  About  Login  Notify  Contact  Search  


References[1] Albrecher, H., Teugels, J.L. and Tichy, R.F. (2001). On gamma series expansion for the timedependent probability of collective ruin. Insurance, Mathematics & Economics, 29, 345–355. MR1874629 [2] Albrecher, H., Constantinescu, C. and Thomann, E. (2008). Sparre Andersen models with risky investments. Working paper. [3] Asmussen, S. (1998). Subexponential asymptotic for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities. The Annals of Applied Probability, 8, 354–374. MR1624933 [4] Asmussen, S. (2000). Ruin Probabilities, World Scientific. MR1794582 [5] Asmussen, S. and Nielsen, H.M. (1995). Ruin probabilities via local adjustment coefficients. Journal of Applied Probability, 32, 736–755. MR1344073 [6] Brekelmans, R. and De Waegenaere, A. (2001). Approximating the finitetime ruin probability under interest force. Insurance, Mathematics & Economics, 29, 217–229. MR1865982 [7] Browne, S. (1995). Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin. Mathematics of Operations Research, 20, 937–958. MR1378114 [8] Cai, J. and Dickson, D. (2003). Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest. Insurance, Mathematics & Economics, 32, 61–71. MR1958769 [9] Cai, J. (2004). Ruin probabilities and penalty functions with stochastic rates of interest. Stochastic Processes and their Applications, 112, 53–78. MR2062567 [10] Cai, J. and Yang, H. (2005). Ruin in the perturbed compound Poisson risk process under interest force. Advances in Applied Probability, 37, 819–835. MR2156562 [11] Cai, J. and Xu, C. (2006). On the decomposition of the ruin probability for a jumpdiffusion surplus process compounded by a geometric Brownian motion. North American Actuarial Journal, 10, 120–132. MR2328640 [12] Cai, J. (2007). On the time value of absolute ruin with debit interest. Advances in Applied Probability, 39, 343–359. MR2341577 [13] Cardoso, R.M.R. and Waters, H.R. (2003). Recursive calculation of finite time ruin probabilities under interest force. Insurance, Mathematics & Economics, 33, 659–676. MR2021240 [14] Chen, Y. and Su, C. (2006). Finite time ruin probability with heavytailed insurance and financial risks. Statistics & Probability Letters, 76, 1812–1820. MR2274145 [15] Chen, Y. and Ng, K.W. (2007). The ruin probability of the renewal model with constant interest force and negatively dependent heavytailed claims. Insurance, Mathematics & Economics, 40, 415–423. MR2310980 [16] Collamore, J.F. (2008). Random recurrence equations and ruin in a Markovdependent stochastic economic environment. To appear in The Annals of Applied Probability. [17] de Kok, T.G. (2003) Ruin probabilities with compounding assets for discrete time finite horizon problems, independent period claim sizes and general premium structure. Insurance, Mathematics & Economics, 33, 645–658. MR2021239 [18] Delbaen, F. and Haezendonck J. (1987). Classical risk theory in an economic environment. Insurance, Mathematics & Economics, 6, 85–116. MR0896414 [19] Embrechts, P. and Schmidli, H. (1994). Ruin estimation for a general insurance risk model. Advances in Applied Probability, 26, 404–422. MR1272719 [20] Frolova, A.G., Kabanov, Y. and Pergamenshchikov, S.M. (2002). In the insurance business risky investments are dangerous. Finance and Stochastics, 6, 227–235. MR1897960 [21] Gaier, J., Grandits, P. and Schachermayer, W. (2003). Asymptotic ruin probabilities and optimal investment. The Annals of Applied Probability, 13, 1054–1076. MR1994044 [22] Gerber, H.U. (1971). Der Einfluss von Zins auf die Ruinwahrscheinlichkeit. Mitteilungen der Schweizerischer Vereinigung der Versicherungsmatematiker, 63–70. [23] Gerber, H.U. and Shiu, E.S.W. (1998). On the time value of ruin, North American Actuarial Journal, 2, 48–78. MR1988433 [24] Gerber, H. and Yang, H. (2007). Absolute ruin probabilities in a jump diffusion risk model with investment. North American Actuarial Journal, 11, 159–169. MR2393866 [25] Gaier, J. and Grandits, P. (2004). Ruin probabilities and investment under interest force in the presence of regularly varying tails. Scandinavian Actuarial Journal, 256–278. MR2081815 [26] Grandits, P. (2004). A Karamatatype theorem and ruin probabilities for an insurer investing proportionally in the stock market. Insurance, Mathematics & Economics, 34, 297–305. MR2053791 [27] Grandits, P. (2005). Minimal ruin probabilities and investment under interest force for a class of subexponential distributions. Scandinavian Actuarial Journal, 401–416. MR2202583 [28] Harrison, J.M. (1977). Ruin problems with compounding assets. Stochastic Processes and their Applications, 5, 67–79. MR0423736 [29] Hipp, C. (2004). Stochastic control with application in insurance. Stochastic methods in finance, Lecture Notes in Math., 1856, 127–164, Springer, Berlin. MR2113722 [30] Hipp, C. and Plum, M. (2000). Optimal investment for insurers. Insurance, Mathematics & Economics, 27, 215–228. MR1801604 [31] Hipp, C. and Schmidli, H. (2004). Asymptotics of ruin probabilities for controlled risk processes in the small claim case. Scandinavian Actuarial Journal, 321–335. MR2096062 [32] Jiang, T. and Yan, HF. (2006). The finitetime ruin probability for the jumpdiffusion model with constant interest force. Acta Mathematicae Applicatae Sinica, 22, 171–176. MR2191727 [33] Kalashnikov, V. and Konstantinides, D. (2000). Ruin under interest force and subexponential claims: a simple treatment. Insurance, Mathematics & Economics, 27, 145–149. MR1796976 [34] Kalashnikov, V. and Norberg, R. (2002). Power tailed ruin probabilities in the presence of risky investments. Stochastic Processes and their Applications, 98, 211–228. MR1887534 [35] Klüppelberg, C. and Stadtmuller, U. (1998). Ruin probabilities in the presence of heavytails and interest rates. Scandinavian Actuarial Journal, 49–58. MR1626664 [36] Knessl, C. and Peters, C. (1994). Exact and asymptotic solutions for the timedependent problem of collective ruin I. SIAM Journal of Applied Mathematics, 54, 1745–1767. MR1301280 [37] Konstantinides, D.G., Tang, Q.H. and Tsitsiashvili, G.S. (2002). Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. Insurance, Mathematics & Economics, 31, 447–460. MR1945543 [38] Konstantinides, D.G., Tang, Q.H. and Tsitsiashvili, G.S. (2004). Twosided bounds for ruin probability under constant interest force. Journal of Mathematical Sciences, 123, 3824–3833. MR2093829 [39] Liu, CS. and Yang, H. (2004). Optimal investment for an insurer to minimize its probability of ruin. North American Actuarial Journal, 8, 11–31. MR2064431 [40] Lundberg, F. (1903). Approximerad Framstilling av Sannolikhetsfunktionen II. Återforsäkring av Kollektivrisker, Almquist & Wiksell, Uppsala. [41] Ma, J. and Sun, X. (2003). Ruin probabilities for insurance models involving investments. Scandinavian Actuarial Journal, 217–237. MR1996926 [42] Norberg, R. (1999). Ruin problems with assets and liabilities of diffusion type. Stochastic Processes and their Applications, 81, 255–269. MR1694553 [43] Nyrhinen, H. (1999). On the ruin probabilities in a general economic environment. Stochastic Processes and their Applications, 89, 319–330. MR1708212 [44] Nyrhinen, H. (2001). Finite and infinite time ruin probabilities in a stochastic economic environment. Stochastic Processes and their Applications, 92, 265–285. MR1817589 [45] Paulsen, J. (1993). Risk theory in a stochastic economic environment. Stochastic Processes and their Applications, 46, 327–361. MR1226415 [46] Paulsen, J. (1998). Sharp conditions for certain ruin in a risk process with stochastic return on investments. Stochastic Processes and their Applications, 75, 135–148. MR1629034 [47] Paulsen, J. (1998). Ruin theory with compounding assets  a survey. Insurance, Mathematics & Economics, 22, 3–16. MR1625827 [48] Paulsen, J. (2002). On Cramérlike asymptotics for risk processes with stochastic return on investments. The Annals of Applied Probability, 12, 1247–1260. MR1936592 [49] Paulsen, J. and Gjessing, H.K. (1997). Ruin theory with stochastic return on investments. Advances in Applied Probability, 29, 965–985. MR1484776 [50] Paulsen, J. and Rasmussen, B.N. (2003). Simulating ruin probabilities for a class of semimartingales by importance sampling methods. Scandinavian Actuarial Journal, 178–216. MR1996925 [51] Paulsen, J., Kasozi, J., and Steigen, A. (2005). A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments. Insurance, Mathematics & Economics, 36, 399–420. MR2152852 [52] Pergamenshchikov, S. and Zeitouny, O. (2006). Ruin probability in the presence of risky investments. Stochastic Processes and their Applications, 116, 267–278. MR2197977 [53] Promislow, S.D. and Young, V.R. (2005). Minimizing the probability of ruin when claims follow Brownian motion with drift. North American Actuarial Journal, 9, 109–128. MR2200024 [54] Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J.L. (1999). Stochastic Processes for Insurance and Finance, Wiley, Chichester. MR1680267 [55] Ruohonen, M. (1980). On the probability of ruin of risk processes approximated by diffusion processes. Scandinavian Actuarial Journal, 113–120. MR0578451 [56] Schäl, M. (2005). Control of ruin probabilities by discretetime investments. Mathematical Methods of Operations Research, 62, 141–158. MR2226972 [57] Schmidli, H. (1994). Risk theory in an economic environment and Markov processes. Mitteilungen der Vereinigung der Versicherungsmatematiker, 51–70. MR1293083 [58] Schmidli, H. (2002). On minimizing the ruin probability by investment and reinsurance. The Annals of Applied Probability, 12, 890–907. MR1925444 [59] Schmidli, H. (2004). Asymptotics of ruin probabilities for risk processes under optimal reinsurance and investment policies: The large claim case. Queueing Systems, 46, 149–157. MR2072280 [60] Schmidli, H. (2005). On optimal investment and subexponential claims. Insurance, Mathematics & Economics, 36, 25–35. MR2122663 [61] Schmidli, H. (2008). Stochastic Control in Insurance, Springer. MR2371646 [62] Segerdahl, C.O. (1942). Über einige risikotheoretische Fragestellungen. Skandinavisk Aktuartidsskrift, 25, 43–83. MR0017902 [63] Sundt, B. and Teugels, J.L. (1995). Ruin estimates under interest force. Insurance, Mathematics & Economics, 16, 7–22. MR1342906 [64] Tang, Q. and Tsitsiashvili, G. (2003). Precise estimates for the ruin probability in finite horizon in a discretetime model with heavytailed insurance and financial risks. Stochastic Processes and their Applications, 108, 299–325. MR2019056 [65] Tang, Q. and Tsitsiashvili, G. (2004). Finite and infinite ruin probabilities in the presence of stochastic returns on investments. Advances in Applied Probability, 36, 1278–1299. MR2119864 [66] Tang, Q. (2004). The ruin probability of a discrete time risk model under constant interest rate with heavy tails. Scandinavian Actuarial Journal, 229–240. MR2064607 [67] Tang, Q. (2005). Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scandinavian Actuarial Journal, 1–5. MR2118521 [68] Tang, Q. (2005). The finite time ruin probability of the compound Poisson model with constant interest force. Journal of Applied Probability, 42, 608–619. MR2157508 [69] Wang, G. and Wu, R. (2001). Distributions for the risk process with a stochastic return on investments. Stochastic Processes and their Applications, 95, 329–341. MR1854031 [70] Wang, G., Yang, H. and Wang, H. (2004). On the distribution of surplus immediately after ruin under interest force and subexponential claims. Insurance, Mathematics & Economics, 35, 703–714. MR2106144 [71] Wang, G. and Wu, R. (2008). The expected discounted penalty function for the perturbed compound Poisson risk process with constant interest. Insurance, Mathematics & Economics, 42, 59–64. MR2392069 [72] Wu, R., Wang, G. and Zhang, C. (2005). On a joint distribution for the risk process with constant interest force. Insurance, Mathematics & Economics, 36, 365–374. MR2152850 [73] Yang, H. and Zhang, L. (2001). The joint distribution of surplus immediately before ruin and the deficit at ruin under interest force. North American Actuarial Journal, 5, 92–103. MR1989761 [74] Yang, H. and Zhang, L. (2006). Ruin problems for a discrete time risk model with random interest rate. Mathematical Methods of Operations Research, 63, 287–299. MR2264750 [75] Yuen, K.C., Wang, G. and Ng, K.W. (2004). Ruin probabilities for a risk process with stochastic return on investments. Stochastic Processes and their Applications, 110, 259–274. MR2040968 [76] Yuen, K.C. and Wang, G. (2005). Some ruin problems for a risk process with stochastic interest. North American Actuarial Journal, 9, 129–142. MR2200025 [77] Yuen, K.C., Wang, G. and Wu, R. (2006). On the renewal risk process with stochastic interest. Stochastic Processes and their Applications, 116, 1496–1510. MR2260745 [78] Zhu, J. and Yang, H. (2008). Estimates for the absolute ruin probability in the compound Poisson risk model with credit and debit interest. Advances in Applied Probability, 40, 818–830. 

Home  Current  Past volumes  About  Login  Notify  Contact  Search Probability Surveys. ISSN: 15495787 