Polynomial Jump-Diffusion Models

References

• Ackerer D, Filipović D (2020a) Linear credit risk models. Finance Stochastics 24(1):169–214.Google Scholar
• Ackerer D, Filipović D (2020b) Option pricing with orthogonal polynomial expansions. Math. Finance 30(1):47–84.Google Scholar
• Ackerer D, Filipović D, Pulido S (2018) The Jacobi stochastic volatility model. Finance Stochastics 22(3):667–700.Google Scholar
• Bakry D, Orevkov S, Zani M (2014) Orthogonal polynomials and diffusion operators. Preprint, submitted September 22, https://arxiv.org/abs/1309.5632.Google Scholar
• Biagini F, Zhang Y (2016) Polynomial diffusion models for life insurance liabilities. Insurance Math. Econom. 71:114–129.Google Scholar
• Callegaro G, Fiorin L, Pallavicini A (2017) Quantization goes polynomial. Preprinted, submitted November 24, https://arxiv.org/abs/1710.11435.Google Scholar
• Çinlar E (2003) Conditional Lévy processes. Comput. Math. Appl. 46(7):993–997.Google Scholar
• Cuchiero C (2011) Affine and polynomial processes. Unpublished doctoral dissertation, ETH Zurich, Zurich, Switzerland.Google Scholar
• Cuchiero C (2019) Polynomial processes in stochastic portfolio theory. Stochastic Processes Their Appl. 129(5):1829–1872.Google Scholar
• Cuchiero C, Keller-Ressel M, Teichmann J (2012) Polynomial processes and their applications to mathematical finance. Finance Stochastics 16(4):711–740.Google Scholar
• Cuchiero C, Larsson M, Svaluto-Ferro S (2018) Polynomial jump-diffusions on the unit simplex. Ann. Appl. Probab. 28(4):2451–2500.Google Scholar
• Cuchiero C, Larsson M, Svaluto-Ferro S (2019) Probability measure-valued polynomial diffusions. Electronic J. Probab. 24(30):1–32.Google Scholar
• Delbaen F, Shirakawa H (2002) An interest rate model with upper and lower bounds. Asia-Pacific Financial Markets 9(3–4):191–209.Google Scholar
• Duffie D, Filipović D, Schachermayer W (2003) Affine processes and applications in finance. Ann. Appl. Probab. 13(3):984–1053.Google Scholar
• Dunkl CF (1992) Hankel transforms associated to finite reflection groups. Contemporary Math. 138:123–138.Google Scholar
• Filipović D, Larsson M (2016) Polynomial diffusions and applications in finance. Finance Stochastics 20(4):931–972.Google Scholar
• Filipović D, Willems S (2019) A term-structure model for dividends and interest rates. Preprint, submitted March 14, https://arxiv.org/abs/1803.02249.Google Scholar
• Filipović D, Mayerhofer E, Schneider P (2013) Density approximations for multivariate affine jump-diffusion processes. J. Econometrics 176(2):93–111.Google Scholar
• Filipović D, Gourier E, Mancini L (2016) Quadratic variance swap models. J. Financial Econom. 119(1):44–68.Google Scholar
• Filipović D, Larsson M, Trolle A (2017) Linear-rational term structure models. J. Finance 72(1):655–704.Google Scholar
• Filipović D, Larsson M, Ware T (2018) Polynomial processes for power prices. Preprint, submitted April 26, https://arxiv.org/abs/1710.10293.Google Scholar
• Filipović D, Larsson M, Pulido S (2019) Markov cubature rules for polynomial processes. Stochastic Processes Their Appl., ePub ahead of print June 17, https://doi.org/10.1016/j.spa.2019.06.010.Google Scholar
• Forman JL, Sørensen M (2008) The Pearson diffusions: A class of statistically tractable diffusion processes. Scandinavian J. Statist. 35(3):438–465.Google Scholar
• Gallardo L, Yor M (2006) A chaotic representation property of the multidimensional Dunkl processes. Ann. Probab. 34(4):1530–1549.Google Scholar
• Gourieroux C, Jasiak J (2006) Multivariate Jacobi process with application to smooth transitions. J. Econometrics 131(1–2):475–505.Google Scholar
• Guasoni P, Wong KC (2018) Asset prices in segmented and integrated markets. Working paper, Boston University, Boston.Google Scholar
• Harrison JM, Pliska SR (1981) Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes Their Appl. 11(3):215–260.Google Scholar
• Hull J, White A (1987) The pricing of options on assets with stochastic volatilities. J. Finance 42(2):281–300.Google Scholar
• Ikeda N, Watanabe S (1989) Stochastic Differential Equations and Diffusion Processes, vol. 24, North-Holland Mathematical Library, 2nd ed. (North-Holland Publishing Co., Amsterdam).Google Scholar
• Jacod J, Shiryaev A (2003) Limit Theorems for Stochastic Processes, 2nd ed. (Springer-Verlag, Berlin, Heidelberg).Google Scholar
• Kallsen J (2006) A didactic note on affine stochastic volatility models. Kabanov Y, Liptser R, Stoyanov J, eds. Stochastic Calculus to Mathematical Finance (Springer‐Verlag, Berlin, Heidelberg), 343–368.Google Scholar
• Kallsen J, Krühner P (2016) On uniqueness of solutions to martingale problems—Counterexamples and sufficient criteria. Preprint, submitted July 11, https://arxiv.org/abs/1607.02998.Google Scholar
• Krühner P, Larsson M (2018) Affine processes with compact state space. Electronic J. Probab. 23(29):1–23.Google Scholar
• Larsen KS, Sørensen M (2007) Diffusion models for exchange rates in a target zone. Math. Finance 17(2):285–306.Google Scholar
• Larsson M, Pulido S (2017) Polynomial diffusions on compact quadric sets. Stochastic Processes Their Appl. 127(3):901–926.Google Scholar
• Li L, Linetsky V (2014) Time-changed Ornstein-Uhlenbeck processes and their applications in commodity derivative models. Math. Finance 24(2):289–330.Google Scholar
• Lions PL, Musiela M (2007) Correlations and bounds for stochastic volatility models. Annales de l’Institut Henri Poincare (C). Nonlinear Anal. 24(1):1–16.Google Scholar
• Mazet O (1997) Classification des semi-groupes de diffusion sur \R associé à une famille de polynômes orthogonaux. Séminaire de probabilités (Strasbourg) 31:40–53.Google Scholar
• Revuz D, Yor M (1999) Continuous Martingales and Brownian Motion, Grundlehren der mathematischen Wissenschaften, vol. 293 (Springer-Verlag, Berlin, Heidelberg).Google Scholar
• Sato K (1999) Lévy Processes and Infinitely Divisible Distributions (Cambridge University Press, Cambridge, MA).Google Scholar
• Schöbel R, Zhu J (1999) Stochastic volatility with an Ornstein–Uhlenbeck process: An extension. Rev. Finance 3(1):23–46.Google Scholar
• Stein EM, Stein JC (1991) Stock price distributions with stochastic volatility: An analytic approach. Rev. Financial Stud. 4(4):727–752.Google Scholar
• Wong E (1964) The construction of a class of stationary Markoff processes. Bellman R, ed. Stochastic Processes in Mathematical Physics and Engineering (American Mathematical Society, Providence, RI), 264–276.Google Scholar
• Zhou H (2003) Itô conditional moment generator and the estimation of short-rate processes. J. Financial Econom. 1(2):250–271.Google Scholar