Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

References

• Ahmadi-Javid A, Pichler A (2017) An analytical study of norms and Banach spaces induced by the entropic value-at-risk. Math. Financial Econom. 11(4):527–550.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber J-M, Heath D, Ku H (2007) Coherent multiperiod risk adjusted values and Bellman’s principle. Ann. Oper. Res. 152(1):5–22.Crossref, Google Scholar
• Bayraktar E, Karatzas I, Yao S (2010) Optimal stopping for dynamic convex risk measures. Illinois J. Math. 54(3):1025–1067.Crossref, Google Scholar
• Bellman RE (1957) Dynamic Programming (Princeton University Press, Princeton, NJ).Google Scholar
• Belomestny D, Krätschmer V (2016) Optimal stopping under model uncertainty: Randomized stopping times approach. Ann. Appl. Probab. 26(2):1260–1295.Crossref, Google Scholar
• Belomestny D, Krätschmer V (2017) Optimal stopping under probability distortions. Math. Oper. Res. 42(3):806–833.Link, Google Scholar
• Bingham NH, Peskir G (2008) Optimal stopping and dynamic programming. Melnick EL, Everitt BS, eds. Encyclopedia of Quantitative Risk Assessment and Analysis (John Wiley & Sons), 1236–1243.Crossref, Google Scholar
• Çavuş O, Ruszczyński A (2014) Risk-averse control of undiscounted transient Markov models. SIAM J. Control Optim. 52(6):3935–3966.Crossref, Google Scholar
• Cheridito P, Kupper M (2009) Recursiveness of indifference prices and translation-invariant preferences. Math. Financial Econom. 2(3):173–188.Crossref, Google Scholar
• 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.Crossref, Google Scholar
• Cheridito P, Delbaen F, Kupper M (2006) Dynamic monetary risk measures for bounded discrete-time processes. Electronic J. Probab. 11(3):57–106.Crossref, Google Scholar
• de Klerk E, Kuhn D, Postek K (2020) Distributionally robust optimization with polynomial densities: Theory, models and algorithms. Math. Programming 181:1–32.Crossref, Google Scholar
• Delage E, Iancu D (2015) Robust multistage decision making. The Operations Research Revolution, TutORials in Operations Research (INFORMS, Catonsville, MD), 20–46.Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• Epstein LG, Schneider M (2003) Recursive multiple-priors. J. Econom. Theory 113(1):1–31.Crossref, Google Scholar
• Föllmer H, Schied A (2004) Stochastic Finance: An Introduction in Discrete Time (De Gruyter, Berlin, Boston).Crossref, Google Scholar
• Garman M (1989) Semper tempus fugit. Risk 2(5):34–35.Google Scholar
• Goldenshluger A, Zeevi A (2021) Optimal stopping of a random sequence with unknown distribution. Math. Oper. Res. 47(1):29–49.Google Scholar
• Guigues V (2018) Multistage stochastic programs with a random number of stages: Dynamic programming equations, solution methods, and application to portfolio selection. Preprint, submitted March 18, https://arxiv.org/abs/1803.06034.Google Scholar
• Hammond PJ (1989) Consistent plans, consequentialism, and expected utility. Econometrica 57(6):1445–1449.Crossref, Google Scholar
• Hanasusanto G, Roitch V, Kuhn D, Wiesemann W (2017) Ambiguous joint chance constraints under mean and dispersion information. Oper. Res. 65(3):751–767.Link, Google Scholar
• Haviv M (1996) On constrained Markov decision processes. Oper. Res. Lett. 19(1):25–28.Crossref, Google Scholar
• Hordijk A (1974) Dynamic Programming and Markov Potential Theory. Mathematical Centre Tracts No. 51 (Centrum Voor Wiskunde en Informatica, Amsterdam).Google Scholar
• Iyengar G (2005) Robust dynamic programming. Math. Oper. Res. 30(2):257–280.Link, Google Scholar
• Jobert A, Rogers LCG (2008) Valuations and dynamic convex risk measures. Math. Finance 18(1):1–22.Crossref, Google Scholar
• Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, vol. 157 (Springer-Verlag, New York).Google Scholar
• Karatzas I, Shreve SE (1998) Methods of Mathematical Finance (Springer-Verlag, New York).Crossref, Google Scholar
• Knight FH (1921) Risk, Uncertainty and Profit (The Riverside Press, Cambridge).Google Scholar
• Kovacevic R, Pflug GCh (2009) Time consistency and information monotonicity of multiperiod acceptability functionals. Albrecher H, Runggaldier WJ, Schachermayer W, eds. Advanced Financial Modelling. Radon Series on Computational and Applied Mathematics, no. 8 (de Gruyter), 347–369.Google Scholar
• Krätschmer V, Schoenmakers J (2010) Representations for optimal stopping under dynamic monetary utility functionals. SIAM J. Financial Math. 1(1):811–832.Crossref, Google Scholar
• Kreps DM, Porteus EL (1978) Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46(1):185–200.Crossref, Google Scholar
• Kupper M, Schachermayer W (2009) Representation results for law invariant time consistent functions. Math. Financial Econom. 2:189–210.Crossref, Google Scholar
• Nilim A, Ghaoui LE (2005) Robust control of Markov decision processes with uncertain transition matrices. Oper. Res. 53(5):780–798.Link, Google Scholar
• Riedel F (2004) Dynamic coherent risk measures. Stochastic Processes Appl. 112(2):185–200.Crossref, Google Scholar
• Rockafellar RT, Wets RJ-B (1997) Variational Analysis (Springer Nature, Switzerland).Google Scholar
• Ruszczyński A (2010) Risk-averse dynamic programming for Markov decision processes. Math. Programming Ser. B 125:235–261.Crossref, Google Scholar
• Ruszczyński A, Shapiro A (2006a) Conditional risk mappings. Math. Oper. Res. 31(3):544–561.Link, Google Scholar
• Ruszczyński A, Shapiro A (2006b) Optimization of convex risk functions. Math. Oper. Res. 31(3):433–452.Link, Google Scholar
• Scarf H (1958) A min-max solution of an inventory problems. Studies in the Mathematical Theory of Inventory and Production (Stanford University Press, Santa Monica), 201–209.Google Scholar
• Shapiro A (2009) On a time consistency concept in risk averse multistage stochastic programming. Oper. Res. Lett. 37(37):143–147.Crossref, Google Scholar
• Shapiro A (2012) Minimax and risk averse multistage stochastic programming. Eur. J. Oper. Res. 219(3):719–726.Crossref, Google Scholar
• Shapiro A (2016) Rectangular sets of probability measures. Oper. Res. 64(2):528–541.Link, Google Scholar
• Shapiro A (2017a) Distributionally robust stochastic programming. SIAM J. Optim. 27(4):2258–2275.Crossref, Google Scholar
• Shapiro A (2017b) Interchangeability principle and dynamic equations in risk averse stochastic programming. Oper. Res. Lett. 45(4):377–381.Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming, Modeling and Theory, 2nd ed. MOS-SIAM Series on Optimization (Society for Industrial and Applied Mathematics).Crossref, Google Scholar
• Shiryaev AN (1978) Optimal Stopping Rules (Springer, New York).Google Scholar
• Wald A (1947) Sequential Analysis (John Wiley & Sons, New York).Google Scholar
• Wald A (1949) Statistical decision functions. Ann. Math. Statist. 20(2):165–205.Crossref, Google Scholar
• Wang T (1999) A class of dynamic risk measures. Technical report, University of British Columbia.Google Scholar
• Weber S (2006) Distribution-invariant risk measures, information, and dynamic consistency. Math. Finance 16(2):419–441.Crossref, Google Scholar
• Weller PA (1978) Consistent intertemporal decision making under uncertainty. Rev. Econom. Stud. 45(2):263–266.Crossref, Google Scholar
• Wiesemann W, Kuhn D, Rustem B (2013) Robust Markov decision processes. Math. Oper. Res. 38(1):153–183.Link, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Zipkin P (2000) Foundation of Inventory Management (McGraw-Hill).Google Scholar