Infinite-dimensional polynomial processes

Abi Jaber, E., Cuchiero, C., Larsson, M., Pulido, S.: A weak solution theory for stochastic Volterra equations of convolution type. Working paper (2019). Available online at arXiv:1909.01166 Abi Jaber, E., El Euch, O.: Markovian structure of the Volterra Heston model. Stat. Probab. Lett. 149, 63–72 (2019) Abi Jaber, E., Larsson, M., Pulido, S.: Affine Volterra processes. Ann. Appl. Probab. 29, 3155–3200 (2019) Ackerer, D., Filipović, D.: Linear credit risk models. Finance Stoch. 24, 169–214 (2020) Ackerer, D., Filipović, D., Pulido, S.: The Jacobi stochastic volatility model. Finance Stoch. 22, 667–700 (2018) Ahdida, A., Alfonsi, A.: A mean-reverting SDE on correlation matrices. Stoch. Process. Appl. 123, 1472–1520 (2013) Alòs, E., León, J.A., Vives, J.: On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility. Finance Stoch. 11, 571–589 (2007) Bayer, C., Friz, P., Gatheral, J.: Pricing under rough volatility. Quant. Finance 16, 887–904 (2016) Beck, C., Becker, S., Grohs, P., Jaafari, N., Jentzen, A.: Solving stochastic differential equations and Kolmogorov equations by means of deep learning. Working paper (2018). Available online at arXiv:1806.00421 Bennedsen, M., Lunde, A., Pakkanen, M.: Decoupling the short-and long-term behavior of stochastic volatility. Working paper (2016). Available online at arXiv:1610.00332 Benth, F., Detering, N., Krühner, P.: Independent increment processes: a multilinearity preserving property. Stochastics (2020), forthcoming. https://doi.org/10.1080/17442508.2020.1802458 Benth, F., Krühner, P.: Representation of infinite-dimensional forward price models in commodity markets. Commun. Math. Stat. 2, 47–106 (2014) Bergomi, L.: Smile dynamics I. Risk 17(9), 117–123 (2004) Bergomi, L.: Smile dynamics II. Risk 18(10), 67–73 (2005) Bergomi, L.: Smile dynamics III. Risk 21(10), 90–96 (2008) Biagini, S., Zhang, Y.: Polynomial diffusion models for life insurance liabilities. Insur. Math. Econ. 71, 114–129 (2016) Blath, J., Casanova, A.G., Kurt, N., Wilke-Berenguer, M.: A new coalescent for seed-bank models. Ann. Appl. Probab. 26, 857–891 (2016) Boedihardjo, H., Geng, X., Lyons, T., Yang, D.: The signature of a rough path: uniqueness. Adv. Math. 293, 720–737 (2016) Buehler, H.: Consistent variance curve models. Finance Stoch. 10, 178–203 (2006) Chen, K.T.: Integration of paths, geometric invariants and a generalized Baker–Hausdorff formula. Ann. Math. 65, 163–178 (1957) Chen, K.T.: Iterated path integrals. Bull. Am. Math. Soc. 83, 831–879 (1977) Chevyrev, I., Lyons, T.: Characteristic functions of measures on geometric rough paths. Ann. Probab. 44, 4049–4082 (2016) Cuchiero, C.: Polynomial processes in stochastic portfolio theory. In: Stochastic Processes and Their Applications, vol. 129, pp. 1829–1872 (2019) Cuchiero, C., Gonon, L., Grigoryeva, L., Ortega, J.-P., Teichmann, J.: Discrete-time signatures and randomness in reservoir computing. Working paper (2020). Available online at arXiv:2010.14615 Cuchiero, C., Keller-Ressel, M., Teichmann, J.: Polynomial processes and their applications to mathematical finance. Finance Stoch. 16, 711–740 (2012) Cuchiero, C., Larsson, M., Svaluto-Ferro, S.: Probability measure-valued polynomial diffusions. Electron. J. Probab. 24(30), 1–32 (2019) Cuchiero, C., Teichmann, J.: Markovian lifts of positive semidefinite affine Volterra type processes. Decis. Econ. Finance 42, 407–448 (2019) Cuchiero, C., Teichmann, J.: Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case. J. Evol. Equ. 20, 1301–1348 (2020) Duffie, D., Filipović, D., Schachermayer, W.: Affine processes and applications in finance. Ann. Appl. Probab. 13, 984–1053 (2003) El Euch, O., Rosenbaum, M.: The characteristic function of rough Heston models. Math. Finance 29, 3–38 (2019) Etheridge, A.: An Introduction to Superprocesses. University Lecture Series, vol. 20. American Mathematical Society, Providence (2000) Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence, 2nd edn. Wiley Series in Probability and Statistics. Wiley, New York (2005) Figalli, A.: Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients. J. Funct. Anal. 254, 109–153 (2008) Filipović, D.: Consistency Problems for Heath–Jarrow–Morton Interest Rate Models. Lecture Notes in Mathematics, vol. 1760. Springer, Berlin (2001) Filipović, D., Gourier, E., Mancini, L.: Quadratic variance swap models. J. Financ. Econ. 119, 44–68 (2016) Filipović, D., Larsson, M.: Polynomial diffusions and applications in finance. Finance Stoch. 20, 931–972 (2016) Filipović, D., Larsson, M.: Polynomial jump-diffusion models. Stoch. Syst. 10, 71–97 (2020) Filipović, D., Tappe, S., Teichmann, J.: Term structure models driven by Wiener processes and Poisson measures: existence and positivity. SIAM J. Financ. Math. 1, 523–554 (2010) Fleming, W.H., Viot, M.: Some measure-valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28, 817–843 (1979) Floret, K.: Natural norms on symmetric tensor products of normed spaces. Note Mat. 17, 153–188 (1997) Friz, P., Hairer, M.: A Course on Rough Paths. Springer, Berlin (2014) Gatheral, J., Jaisson, T., Rosenbaum, M.: Volatility is rough. Quant. Finance 18, 933–949 (2018) Heitzinger, C., Pammer, G., Rigger, S.: Cubature formulas for multisymmetric functions and applications to stochastic partial differential equations. SIAM/ASA J. Uncertain. Quantificat. 6, 213–242 (2018) Horvath, B., Jacquier, A., Tankov, P.: Volatility options in rough volatility models. SIAM J. Financ. Math. 11, 437–469 (2020) Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes, 2nd edn. Springer, Berlin (2003) Jacquier, A., Martini, C., Muguruza, A.: On VIX futures in the rough Bergomi model. Quant. Finance 18, 45–61 (2018) Janson, S.: Tensor norms on ordered normed spaces, polarization constants, and exchangeable distributions. Working paper (2018). Available online at arXiv:1811.02450 Kidger, P., Bonnier, P., Perez Arribas, I., Salvi, C., Lyons, T.: Deep signature transforms. In: Wallach, H., et al. (eds.), Advances in Neural Information Processing Systems, vol. 32, pp. 3105–3115. Curran Associates, Red Hook (2019) Kimura, M.: Diffusion models in population genetics. J. Appl. Probab. 1, 177–232 (1964) Kotelenez, P.: Comparison methods for a class of function valued stochastic partial differential equations. Probab. Theory Relat. Fields 93, 1–19 (1992) Kunze, M.: On a class of martingale problems on Banach spaces. Electron. J. Probab. 18, 104 (2013) Larsson, M., Svaluto-Ferro, S.: Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces. Electron. J. Probab. 25, 1–25 (2020) Levin, D., Lyons, T., Ni, H.: Learning from the past, predicting the statistics for the future, learning an evolving system. Working paper (2013). Available online at arXiv:1309.0260 Lyons, T.J.: Differential equations driven by rough signals. Rev. Mat. Iberoam. 14, 215–310 (1998) Milian, A.: Comparison theorems for stochastic evolution equations. Stoch. Int. J. Probab. Stoch. Process. 72, 79–108 (2002) Papavasiliou, A., Ladroue, C.: Parameter estimation for rough differential equations. Ann. Stat. 39, 2047–2073 (2011) Perez Arribas, I., Salvi, C., Szpruch, L.: Sig-SDEs model for quantitative finance. Working paper (2020). Available online at arXiv:2006.00218 Ryan, R.: Introduction to Tensor Products of Banach Spaces. Springer, Berlin (2013) Schmidt, T., Tappe, S., Yu, W.: Infinite dimensional affine processes. Stoch. Process. Appl. 130, 7131–7169 (2020)