메뉴 건너뛰기




Volumn 46, Issue 3, 2008, Pages 1580-1601

Maximal use of central differencing for Hamilton-Jacobi-Bellman PDEs in finance

Author keywords

Central differencing; Finance; Monotone scheme; Nonlinear Hamilton Jacobi Bellman partial differential equations; Stochastic control

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; IMAGE SEGMENTATION; MEATS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 55349092691     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/060675186     Document Type: Article
Times cited : (75)

References (32)
  • 1
    • 14244265454 scopus 로고    scopus 로고
    • Nonlinear integro-differential evolution problems arising in option pricing: A viscosity solution approach
    • A. L. AMADORI, Nonlinear integro-differential evolution problems arising in option pricing: A viscosity solution approach, Differential Integral Equations, 16 (2003), pp. 787-811.
    • (2003) Differential Integral Equations , vol.16 , pp. 787-811
    • AMADORI, A.L.1
  • 3
    • 84953009457 scopus 로고
    • Pricing and hedging derivative securities in markets with uncertain volatilities
    • M. AVELLANEDA, A. LEVY, AND A. PARAS, Pricing and hedging derivative securities in markets with uncertain volatilities, Appl. Math. Finance, 2 (1995), pp. 73-88.
    • (1995) Appl. Math. Finance , vol.2 , pp. 73-88
    • AVELLANEDA, M.1    LEVY, A.2    PARAS, A.3
  • 4
    • 0041753938 scopus 로고    scopus 로고
    • Convergence of numerical schemes for degenerate parabolic equations arising in finance
    • L. C. G. Rogers and D. Talay, eds, Cambridge University Press, Cambridge, UK
    • G. B ARLES, Convergence of numerical schemes for degenerate parabolic equations arising in finance, in Numerical Methods in Finance, L. C. G. Rogers and D. Talay, eds., Cambridge University Press, Cambridge, UK, 1997, pp. 1-21.
    • (1997) Numerical Methods in Finance , pp. 1-21
    • ARLES, G.B.1
  • 5
    • 84963420752 scopus 로고
    • The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems
    • G. BARLES AND J. BURDEAU, The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems, Comm. Partial Differential Equations, 20 (1995), pp. 129-178.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 129-178
    • BARLES, G.1    BURDEAU, J.2
  • 6
    • 0001241353 scopus 로고
    • Convergence of numerical shemes for parabolic equations arising in finance theory
    • G. BARLES, C. DAHER, AND M. ROMANO, Convergence of numerical shemes for parabolic equations arising in finance theory, Math. Models Methods Appl. Sci., 5 (1995), pp. 125-143.
    • (1995) Math. Models Methods Appl. Sci , vol.5 , pp. 125-143
    • BARLES, G.1    DAHER, C.2    ROMANO, M.3
  • 7
    • 38849122631 scopus 로고    scopus 로고
    • Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
    • G. BARLES AND E. JAKOBSEN, Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations, Math. Comp., 76 (2007), pp. 1861-1893.
    • (2007) Math. Comp , vol.76 , pp. 1861-1893
    • BARLES, G.1    JAKOBSEN, E.2
  • 8
    • 0001700806 scopus 로고    scopus 로고
    • A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications
    • G. BARLES AND E. ROUY, A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications, Comm. Partial Differential Equations, 23 (1998), pp. 1945-2033.
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 1945-2033
    • BARLES, G.1    ROUY, E.2
  • 9
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear equations
    • G. BARLES AND P. SOUGANIDIS, Convergence of approximation schemes for fully nonlinear equations, Asymptotic Anal., 4 (1991), pp. 271-283.
    • (1991) Asymptotic Anal , vol.4 , pp. 271-283
    • BARLES, G.1    SOUGANIDIS, P.2
  • 11
    • 2942747037 scopus 로고    scopus 로고
    • Optimal portfolio management management rules in a non-Gaussian market with durability and intertemporal substitution
    • F. E. BENTH, K. KARLSEN, AND K. REIKVAM, Optimal portfolio management management rules in a non-Gaussian market with durability and intertemporal substitution, Finance Stoch., 5 (2001), pp. 447-467.
    • (2001) Finance Stoch , vol.5 , pp. 447-467
    • BENTH, F.E.1    KARLSEN, K.2    REIKVAM, K.3
  • 12
    • 21844481611 scopus 로고
    • Option pricing with differential interest rates
    • Y. BERGMAN, Option pricing with differential interest rates, Review Financial Studies, 8 (1995), pp. 475-500.
    • (1995) Review Financial Studies , vol.8 , pp. 475-500
    • BERGMAN, Y.1
  • 13
    • 27144473473 scopus 로고    scopus 로고
    • Ruin in the perturbed compound Poisson risk process under interest force
    • J. CAI AND H. YANG, Ruin in the perturbed compound Poisson risk process under interest force, Adv. in Appl. Probab., 37 (2005), pp. 819-835.
    • (2005) Adv. in Appl. Probab , vol.37 , pp. 819-835
    • CAI, J.1    YANG, H.2
  • 14
    • 33645934793 scopus 로고    scopus 로고
    • A. CAIRNS, D. BLAKE, AND K. DOWD, Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, J. Econom. Dynam. Control, 30 (2006), pp. 843-877.
    • A. CAIRNS, D. BLAKE, AND K. DOWD, Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, J. Econom. Dynam. Control, 30 (2006), pp. 843-877.
  • 15
    • 34547313500 scopus 로고    scopus 로고
    • Combined stochastic control and optimal stopping and application to numerical approximation of combined stochastic and impulse control
    • J. P. CHANCELLOR, B. OKSENDAL, AND A. SULEM, Combined stochastic control and optimal stopping and application to numerical approximation of combined stochastic and impulse control, Stochastic Financial Math., 237 (2002), pp. 149-173.
    • (2002) Stochastic Financial Math , vol.237 , pp. 149-173
    • CHANCELLOR, J.P.1    OKSENDAL, B.2    SULEM, A.3
  • 17
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. CRANDALL, H. ISHII, AND P. L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), pp. 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • CRANDALL, M.G.1    ISHII, H.2    LIONS, P.L.3
  • 18
    • 44649139964 scopus 로고    scopus 로고
    • Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
    • Winter, pp
    • P. FORSYTH AND G. LABAHN, Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance, J. Computational Finance, 11 (2007/2008, Winter), pp. 1-43.
    • (2007) J. Computational Finance , vol.11 , pp. 1-43
    • FORSYTH, P.1    LABAHN, G.2
  • 21
    • 84944830176 scopus 로고
    • Option pricing and replication with transaction costs
    • H. E. LELAND, Option pricing and replication with transaction costs, J. Finance, 40 (1985), pp. 1283-1301.
    • (1985) J. Finance , vol.40 , pp. 1283-1301
    • LELAND, H.E.1
  • 23
    • 47249126948 scopus 로고    scopus 로고
    • Optimal risk control and dividend policies under excess of loss reinsurance
    • M. MNIF AND A. SULEM, Optimal risk control and dividend policies under excess of loss reinsurance, Stoch. Stoch. Rep., 77 (2005), pp. 455-476.
    • (2005) Stoch. Stoch. Rep , vol.77 , pp. 455-476
    • MNIF, M.1    SULEM, A.2
  • 27
    • 0038150517 scopus 로고    scopus 로고
    • Numerical convergence properties of option pricing PDEs with uncertain volatility
    • D. POOLEY, P. FORSYTH, AND K. VETZAL, Numerical convergence properties of option pricing PDEs with uncertain volatility, IMA J. Numer. Anal., 23 (2003), pp. 241-267.
    • (2003) IMA J. Numer. Anal , vol.23 , pp. 241-267
    • POOLEY, D.1    FORSYTH, P.2    VETZAL, K.3
  • 28
    • 0036392392 scopus 로고    scopus 로고
    • On minimizing the ruin probability by investment and reinsurance
    • H. SCHMIDLI, On minimizing the ruin probability by investment and reinsurance, Ann. Appl. Probab., 12 (2002), pp. 890-907.
    • (2002) Ann. Appl. Probab , vol.12 , pp. 890-907
    • SCHMIDLI, H.1
  • 29
    • 55349116671 scopus 로고    scopus 로고
    • S. SHR.EVE AND J. VECER, Options on a traded account: Vacation calls, vacation puts, and passport options, Finance Stoch., 4 (2000), pp. 255-274.
    • S. SHR.EVE AND J. VECER, Options on a traded account: Vacation calls, vacation puts, and passport options, Finance Stoch., 4 (2000), pp. 255-274.
  • 31
    • 33751098024 scopus 로고    scopus 로고
    • Hedging with a correlated asset: Solution of a nonlinear pricing PDE
    • H. WINDCLIFF, J. WANG, P. FORSYTH, AND K. VETZAL, Hedging with a correlated asset: Solution of a nonlinear pricing PDE, J. Comput. Appl. Math., 200 (2007), pp. 86-115.
    • (2007) J. Comput. Appl. Math , vol.200 , pp. 86-115
    • WINDCLIFF, H.1    WANG, J.2    FORSYTH, P.3    VETZAL, K.4
  • 32
    • 39449127987 scopus 로고    scopus 로고
    • Multi-factor financial derivatives on finite domains
    • Y.-L. ZHU AND J. LI, Multi-factor financial derivatives on finite domains, Commun. Math. Sci., l (2003), pp. 343-359.
    • (2003) Commun. Math. Sci , vol.50 , pp. 343-359
    • ZHU, Y.-L.1    LI, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.