Risk-Averse Optimal Control in Continuous Time by Nesting Risk Measures

Published Online:https://doi.org/10.1287/moor.2022.1314

References

  • [1] Ahmadi-Javid A (2012) Entropic value-at-risk: A new coherent risk measure. J. Optim. Theory Appl. 155(3):1105–1123.CrossrefGoogle Scholar
  • [2] Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math. Finance 9:203–228.CrossrefGoogle Scholar
  • [3] Barrieu P, Karoui NE (2004) Optimal derivatives design under dynamic risk measures. Contemporary Mathematics, vol. 351 (American Mathematical Society), 13–25.Google Scholar
  • [4] Breuer T, Csiszár I (2013) Measuring distribution model risk. Math. Finance 26(2):395–411.Google Scholar
  • [5] Çavuş O, Ruszczyński A (2014) Risk-averse control of undiscounted transient Markov models. SIAM J. Control Optim. 52(6):3935–3966.CrossrefGoogle Scholar
  • [6] Cheridito P, Kupper M (2011) Composition of time-consistent dynamic monetary risk measures in discrete time. Internat. J. Theoret. Appl. Finance 14(1):137–162.CrossrefGoogle Scholar
  • [7] Coquet F, Hu Y, Peng S (2002) Filtration-consistent nonlinear expectations and related g-expectations. Probab. Theory Related Fields 123:1–27.CrossrefGoogle Scholar
  • [8] Crandall MG, Lions P-L (1983) Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277(1):1–42.CrossrefGoogle Scholar
  • [9] De Lara M, Leclère V (2016) Building up time-consistency for risk measures and dynamic optimization. Eur. J. Oper. Res. 249:177–187.CrossrefGoogle Scholar
  • [10] Dentcheva D, Ruszczyński A (2018) Time-coherent risk measures for continuous-time Markov chains. SIAM J. Financial Math. 9(2):690–715.CrossrefGoogle Scholar
  • [11] Fan J, Ruszczyński A (2018) Process-based risk measures and risk-averse control of discrete-time systems. Math. Programming 191(1):113–140.Google Scholar
  • [12] Fleming WH, Soner HM (2006) Controlled Markov Processes and Viscosity Solutions, 2nd ed. (Springer).Google Scholar
  • [13] Frittelli M, Rosazza Gianin E (2004) Dynamic convex risk measures. New Risk Measures for the 21st Century (John Wiley & Sons), 227–248.Google Scholar
  • [14] Guigues V, Römisch W (2012) SDDP for multistage stochastic linear programs based on spectral risk measures. Oper. Res. Lett. 40(5):313–318.CrossrefGoogle Scholar
  • [15] Haskell WB, Jain R (2015) A convex analytic approach to risk-aware Markov decision processes. SIAM J. Control Optim. 53(3):1569–1598.CrossrefGoogle Scholar
  • [16] Haskell WB, Jain R, Kalathil D (2016) Empirical dynamic programming. Math. Oper. Res. 41(2):402–429.LinkGoogle Scholar
  • [17] Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics (Springer-Verlag, New York).Google Scholar
  • [18] Maggioni F, Allevi E, Bertocchi M (2012) Measures of information in multistage stochastic programming. Sakalauskas L, Tomasgard A, Wallace SW, eds. Internat. Workshop Stochastic Programming Implementation Advanced Appl. (Association of Lithuanian Serials), 78–82.Google Scholar
  • [19] Ogryczak W, Ruszczyński A (2002) Dual stochastic dominance and related mean-risk models. SIAM J. Optim. 13(1):60–78.CrossrefGoogle Scholar
  • [20] Øksendal B (2003) Stochastic Differential Equations, 6th ed. (Springer, Berlin).CrossrefGoogle Scholar
  • [21] Pardoux E, Peng SG (1990) Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14:55–61.CrossrefGoogle Scholar
  • [22] Peng S (2004) Nonlinear expectations, nonlinear evaluations and risk measures. Lecture Notes in Mathematics (Springer, Berlin Heidelberg), 165–253.Google Scholar
  • [23] Pflug GCh, Pichler A (2016) Time-consistent decisions and temporal decomposition of coherent risk functionals. Math. Oper. Res. 41(2):682–699.LinkGoogle Scholar
  • [24] Philpott AB, de Matos VL (2012) Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion. Eur. J. Oper. Res. 218(2):470–483.CrossrefGoogle Scholar
  • [25] Pichler A, Schlotter R (2020) Entropy based risk measures. Eur. J. Oper. Res. 285(1):223–236.CrossrefGoogle Scholar
  • [26] Pichler A, Schlotter R (2021) Quantification of risk in classical models of finance. Quant. Finance 22(1):31–45.CrossrefGoogle Scholar
  • [27] Pichler A, Liu RP, Shapiro A (2021) Risk-averse stochastic programming: Time consistency and optimal stopping. Oper. Res. 70(4):2439–2455.LinkGoogle Scholar
  • [28] Rosazza Gianin E (2006) Risk measures via g-expectations. Insurance Math. Econom. 39(1):19–34.CrossrefGoogle Scholar
  • [29] Ruszczyński A, Shapiro A (2006) Conditional risk mappings. Math. Oper. Res. 31(3):544–561.LinkGoogle Scholar
  • [30] Ruszczyński A, Yao J (2015) A risk-averse analog of the Hamilton–Jacobi–Bellman equation. Proc. Conf. Control Its Appl. (Society for Industrial & Applied Mathematics), 462–468.Google Scholar
  • [31] Ruszczyński A, Yao J (2020) A dual method for evaluation of dynamic risk in diffusion processes. ESAIM Control Optim. Calculus Variations 26:96.CrossrefGoogle Scholar
  • [32] Xin L, Shapiro A (2012) Bounds for nested law invariant coherent risk measures. Oper. Res. Lett. 40:431–435.CrossrefGoogle Scholar
  • [33] Zhang J (2017) Backward Stochastic Differential Equations (Springer, New York).CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.