Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

Published Online:https://doi.org/10.1287/moor.2022.1262

References

  • [1] Avanesyan L, Shkolnikov M, Sircar R (2020) Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem. Finance Stochastics 24(4):981–1011.CrossrefGoogle Scholar
  • [2] Briand P, Confortola F (2008) Quadratic BSDEs with random terminal time and elliptic PDEs in infinite dimension. Electron. J. Probab. 13:1529–1561.Google Scholar
  • [3] Chong W, Liang G (2018) Optimal investment and consumption with forward preferences and uncertain parameters. Preprint, submitted July 3, https://arxiv.org/abs/1807.01186.Google Scholar
  • [4] Chong W, Hu Y, Liang G, Zariphopoulou T (2019) An ergodic BSDE approach to forward entropic risk measures: Representation and large-maturity behavior. Finance Stochastics 23(1):239–273.CrossrefGoogle Scholar
  • [5] Choulli T, Ma J (2017) Explicit description of HARA forward utilities and their optional portfolios. Theory Probab. Appl. 61(1):57–93.CrossrefGoogle Scholar
  • [6] Cohen S, Hu Y (2013) Ergodic BSDEs driven by Markov chains. SIAM J. Control Optim. 51(5):4138–4168.CrossrefGoogle Scholar
  • [7] Jacod J (1979) Calcul Stochastique et Problèmes de Martingales (Springer-Verlag, New York).CrossrefGoogle Scholar
  • [8] Jacod J, Shiryaev A (1987) Limit Theorems for Stochastic Processes (Springer-Verlag, New York).CrossrefGoogle Scholar
  • [9] Karatzas I, Kardaras C (2007) The numéraire portfolio in semimartingale financial models. Finance Stochastics 11(4):447–493.CrossrefGoogle Scholar
  • [10] Kardaras C (2009) No-free-lunch equivalences for exponential Lévy models under convex constraints on investment. Math. Finance 19(2):161–187.CrossrefGoogle Scholar
  • [11] Li J, Zhao N (2019) Representation of asymptotic values for nonexpansive stochastic control systems. Stochastic Processes Their Appl. 129(2):634–673.CrossrefGoogle Scholar
  • [12] Liang G, Zariphopoulou T (2017) Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE. SIAM J. Financial Math. 8(1):344–372.CrossrefGoogle Scholar
  • [13] Liptser R, Shiryayev A (1986) Theory of Martingales (Kluwer Academic Publishers, Dordrecht, The Netherlands).Google Scholar
  • [14] Merton R (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econom. Statist. 51(3):247–257.CrossrefGoogle Scholar
  • [15] Musiela M, Zariphopoulou T (2008) Optimal asset allocation under forward exponential criteria. Markov Processes and Related Topics: A Festschrift for T.G. Kurtz. Institute of Mathematical Statistics Collections, vol. 4 (Institute of Mathematical Statistics, Beachwood, OH), 285–300.CrossrefGoogle Scholar
  • [16] Musiela M, Zariphopoulou T (2010) Portfolio choice under space-time monotone performance criteria. SIAM J. Financial Math. 1(1):326–365.CrossrefGoogle Scholar
  • [17] Musiela M, Zariphopoulou T (2010) Stochastic partial differential equations and portfolio choice. Chiarella C, Novikov A, eds. Contemporary Quantitative Finance (Springer, Berlin), 195–216.CrossrefGoogle Scholar
  • [18] Nadtochiy S, Tehranchi M (2017) Optimal investment for all time horizons and Martin boundary of space-time diffusions. Math. Finance 27(2):438–470.CrossrefGoogle Scholar
  • [19] Nadtochiy S, Zariphopoulou T (2014) A class of homothetic forward investment performance processes with non-zero volatility. Kabanov Y, Rutkowski M, Zariphopoulou T, eds. Inspired by Finance (Springer, New York), 475–504.CrossrefGoogle Scholar
  • [20] Nutz M (2012) The Bellman equation for power utility maximization with semimartingales. Ann. Appl. Probab. 22(1):363–406.CrossrefGoogle Scholar
  • [21] Nutz M (2012) Power utility maximization in constrained exponential Lévy models. Math. Finance 22(4):690–709.CrossrefGoogle Scholar
  • [22] Richou A (2009) Ergodic BSDEs and related PDEs with Neumann boundary conditions. Stochastic Processes Their Appl. 119(9):2945–2969.CrossrefGoogle Scholar
  • [23] Rockafellar R (1970) Convex Analysis (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • [24] Shkolnikov M, Sircar R, Zariphopoulou T (2016) Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations. SIAM J. Financial Math. 7(1):588–618.CrossrefGoogle Scholar
  • [25] Strub M, Zhou X (2021) Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes. Finance Stochastics 25(2):331–358.CrossrefGoogle Scholar
  • [26] Zitkovic G (2009) A dual characterization of self-generation and exponential forward performances. Ann. Appl. Probab. 19(6):2176–2210.CrossrefGoogle Scholar
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