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Volumn 46, Issue 1, 2010, Pages 52-66

An insurance risk model with stochastic volatility

Author keywords

Gerber Shiu expected discounted penalty function; Integro differential equation; Ornstein Uhlenbeck process; Perturbed compound Poisson risk process; Phase type distribution; Singular perturbation theory; Stochastic volatility

Indexed keywords


EID: 74249113918     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2009.03.006     Document Type: Article
Times cited : (6)

References (31)
  • 1
    • 0036044480 scopus 로고    scopus 로고
    • Risk theory with a nonlinear dividend barrier
    • Albrecher H., and Kainhofer R. Risk theory with a nonlinear dividend barrier. Computing 68 (2002) 289-311
    • (2002) Computing , vol.68 , pp. 289-311
    • Albrecher, H.1    Kainhofer, R.2
  • 4
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • Black F., and Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy 81 3 (1973) 637-654
    • (1973) Journal of Political Economy , vol.81 , Issue.3 , pp. 637-654
    • Black, F.1    Scholes, M.2
  • 6
    • 27144473473 scopus 로고    scopus 로고
    • Ruin in the perturbed compound Poisson risk process under interest force
    • Cai J., and Yang H.L. Ruin in the perturbed compound Poisson risk process under interest force. Advances in Applied Probability 37 (2005) 819-835
    • (2005) Advances in Applied Probability , vol.37 , pp. 819-835
    • Cai, J.1    Yang, H.L.2
  • 7
    • 34547186065 scopus 로고    scopus 로고
    • An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model
    • Chen Y.T., Lee C.F., and Sheu Y.C. An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model. Finance and Stochastics 11 (2007) 323-355
    • (2007) Finance and Stochastics , vol.11 , pp. 323-355
    • Chen, Y.T.1    Lee, C.F.2    Sheu, Y.C.3
  • 8
    • 2442453507 scopus 로고    scopus 로고
    • Stochastic volatility corrections for interest rate derivatives
    • Cotton P., Fouque J.P., Papanicolaou G., and Sircar R. Stochastic volatility corrections for interest rate derivatives. Mathematical Finance 14 2 (2004) 173-200
    • (2004) Mathematical Finance , vol.14 , Issue.2 , pp. 173-200
    • Cotton, P.1    Fouque, J.P.2    Papanicolaou, G.3    Sircar, R.4
  • 9
    • 0001912797 scopus 로고
    • Risk theory for the compound Poisson process that is perturbed by diffusion
    • Dufresne F., and Gerber H.U. Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance: Mathematics and Economics 10 (1991) 51-59
    • (1991) Insurance: Mathematics and Economics , vol.10 , pp. 51-59
    • Dufresne, F.1    Gerber, H.U.2
  • 11
    • 34548050921 scopus 로고    scopus 로고
    • On the expected discounted penalty function for Lévy risk processes
    • Garrido J., and Morales M. On the expected discounted penalty function for Lévy risk processes. North American Actuarial Journal 10 4 (2006) 196-218
    • (2006) North American Actuarial Journal , vol.10 , Issue.4 , pp. 196-218
    • Garrido, J.1    Morales, M.2
  • 12
    • 0032113775 scopus 로고    scopus 로고
    • On the discounted penalty at ruin in a jump-diffusion and the perpetual put option
    • Gerber H.U., and Landry B. On the discounted penalty at ruin in a jump-diffusion and the perpetual put option. Insurance: Mathematics and Economics 22 (1998) 263-276
    • (1998) Insurance: Mathematics and Economics , vol.22 , pp. 263-276
    • Gerber, H.U.1    Landry, B.2
  • 14
    • 0037836721 scopus 로고
    • A closed-form solution for options with stochastic volatility with applications to bond and currency options
    • Heston S.L. A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies 6 2 (1993) 327-343
    • (1993) The Review of Financial Studies , vol.6 , Issue.2 , pp. 327-343
    • Heston, S.L.1
  • 15
    • 57649213791 scopus 로고    scopus 로고
    • Asymptotic pricing of commodity derivatives using stochastic volatility spot models
    • Hikspoors S., and Jaimungal S. Asymptotic pricing of commodity derivatives using stochastic volatility spot models. Applied Mathematical Finance 15 (2008) 449-477
    • (2008) Applied Mathematical Finance , vol.15 , pp. 449-477
    • Hikspoors, S.1    Jaimungal, S.2
  • 17
    • 84993608428 scopus 로고
    • Corporate debt value, bond covenants, and optimal capital structure
    • Leland H.E. Corporate debt value, bond covenants, and optimal capital structure. Journal of Finance 49 (1994) 1213-1252
    • (1994) Journal of Finance , vol.49 , pp. 1213-1252
    • Leland, H.E.1
  • 18
    • 0001973398 scopus 로고    scopus 로고
    • Analysis of a defective renewal equation arising in ruin theory
    • Lin X.S., and Willmot G.E. Analysis of a defective renewal equation arising in ruin theory. Insurance: Mathematics and Economics 25 (1999) 63-84
    • (1999) Insurance: Mathematics and Economics , vol.25 , pp. 63-84
    • Lin, X.S.1    Willmot, G.E.2
  • 19
    • 0001858607 scopus 로고    scopus 로고
    • The moments of the time of ruin, the surplus before ruin, and the deficit at ruin
    • Lin X.S., and Willmot G.E. The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Insurance: Mathematics and Economics 27 (2000) 19-44
    • (2000) Insurance: Mathematics and Economics , vol.27 , pp. 19-44
    • Lin, X.S.1    Willmot, G.E.2
  • 20
    • 84864290365 scopus 로고    scopus 로고
    • Numerical solution of some second order integro-differential equations arising in ruin theory
    • Samos, Greece
    • Makroglou, A., 2004. Numerical solution of some second order integro-differential equations arising in ruin theory. In: Proceedings of the 3rd Conference in Actuarial Science and Finance, Samos, Greece
    • (2004) Proceedings of the 3rd Conference in Actuarial Science and Finance
    • Makroglou, A.1
  • 21
    • 74249119893 scopus 로고    scopus 로고
    • Computational treatment of the integrodifferential equations of collective non-ruin; the ultimate non-ruin case
    • Corduneanu C., and Sandberg I.W. (Eds), CRC Press
    • Makroglou A., Harper W., and Smith B. Computational treatment of the integrodifferential equations of collective non-ruin; the ultimate non-ruin case. In: Corduneanu C., and Sandberg I.W. (Eds). Volterra Equations and Applications (1999), CRC Press 341-350
    • (1999) Volterra Equations and Applications , pp. 341-350
    • Makroglou, A.1    Harper, W.2    Smith, B.3
  • 24
    • 40949158855 scopus 로고    scopus 로고
    • Approximations for the moments of ruin time in the compound Poisson model
    • Pitts S., and Politis K. Approximations for the moments of ruin time in the compound Poisson model. Insurance: Mathematics and Economics 42 (2008) 668-679
    • (2008) Insurance: Mathematics and Economics , vol.42 , pp. 668-679
    • Pitts, S.1    Politis, K.2
  • 25
    • 34548022134 scopus 로고    scopus 로고
    • Approximations for the Gerber-Shiu expected discounted penalty function in the compound Poisson risk model
    • Pitts S., and Politis K. Approximations for the Gerber-Shiu expected discounted penalty function in the compound Poisson risk model. Advances in Applied Probability 39 (2007) 385-406
    • (2007) Advances in Applied Probability , vol.39 , pp. 385-406
    • Pitts, S.1    Politis, K.2
  • 26
    • 29144474120 scopus 로고    scopus 로고
    • The expected value of the time of ruin and the moments of the discounted deficit at ruin in the perturbed classical risk process
    • Ren J.D. The expected value of the time of ruin and the moments of the discounted deficit at ruin in the perturbed classical risk process. Insurance: Mathematics and Economics 37 (2005) 505-521
    • (2005) Insurance: Mathematics and Economics , vol.37 , pp. 505-521
    • Ren, J.D.1
  • 28
    • 0036192793 scopus 로고    scopus 로고
    • A generalized defective renewal equation for the surplus process perturbed by diffusion
    • Tsai C.C.L., and Willmot G.E. A generalized defective renewal equation for the surplus process perturbed by diffusion. Insurance: Mathematics and Economics 30 (2002) 51-66
    • (2002) Insurance: Mathematics and Economics , vol.30 , pp. 51-66
    • Tsai, C.C.L.1    Willmot, G.E.2
  • 30
    • 43849089197 scopus 로고    scopus 로고
    • On the class of Erlang mixtures with risk theoretic applications
    • Willmot G.E., and Woo J.K. On the class of Erlang mixtures with risk theoretic applications. North American Actuarial Journal 11 2 (2007) 99-118
    • (2007) North American Actuarial Journal , vol.11 , Issue.2 , pp. 99-118
    • Willmot, G.E.1    Woo, J.K.2
  • 31
    • 0035272526 scopus 로고    scopus 로고
    • Spectrally negative Lévy processes with applications in risk theory
    • Yang H.L., and Zhang L.Z. Spectrally negative Lévy processes with applications in risk theory. Advances in Applied Probability 33 (2001) 281-291
    • (2001) Advances in Applied Probability , vol.33 , pp. 281-291
    • Yang, H.L.1    Zhang, L.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.