Dynamically Optimal Portfolios for Monotone Mean-Variance Preferences

References

• [1] Bellini F, Frittelli M (2002) On the existence of minimax martingale measures. Math. Finance 12(1):1–21.Crossref, Google Scholar
• [2] Bender C, Niethammer CR (2008) On q-optimal martingale measures in exponential Lévy models. Finance Stochastics 12(3):381–410.Crossref, Google Scholar
• [3] Biagini S, Černý A (2011) Admissible strategies in semimartingale portfolio selection. SIAM J. Control Optim. 49(1):42–72.Crossref, Google Scholar
• [4] Biagini S, Černý A (2020) Convex duality and Orlicz spaces in expected utility maximization. Math. Finance 30(1):85–127.Crossref, Google Scholar
• [5] Black F, Perold AF (1992) Theory of constant proportion portfolio insurance. J. Econom. Dynam. Control 16(3):403–426.Crossref, Google Scholar
• [6] Cawston S, Vostrikova L (2014) An f-divergence approach for optimal portfolios in exponential Lévy models. Kabanov Y, Rutkowski M, Zariphopoulou T, eds. Inspired by Finance (Springer, Cham, Switzerland), 83–101.Crossref, Google Scholar
• [7] Černý A (2003) Generalized Sharpe ratios and asset pricing in incomplete markets. Rev. Finance 7(2):191–233.Crossref, Google Scholar
• [8] Černý A (2020a) The Hansen ratio in mean–variance portfolio theory. Preprint, submitted July 31, https://arxiv.org/abs/2007.15980.Google Scholar
• [9] Černý A (2020b) Semimartingale theory of monotone mean–variance portfolio allocation. Math. Finance 30(3):1168–1178.Google Scholar
• [10] Černý A, Kallsen J (2007) On the structure of general mean-variance hedging strategies. Ann. Probab. 35(4):1479–1531.Crossref, Google Scholar
• [11] Černý A, Ruf J (2021a) Pure-jump semimartingales. Bernoulli 27(4):2624–2648.Crossref, Google Scholar
• [12] Černý A, Ruf J (2021b) Simplified stochastic calculus with applications in economics and finance. Eur. J. Oper. Res. 293(2):547–560.Crossref, Google Scholar
• [13] Černý A, Ruf J (2022) Simplified stochastic calculus via semimartingale representations. Electronic J. Probab. 27:1–32.Crossref, Google Scholar
• [14] Černý A, Ruf J (2023) Simplified calculus for semimartingales: Multiplicative compensators and changes of measure. Stochastic Processes Appl. 161:572–602.Crossref, Google Scholar
• [15] Černý A, Maccheroni F, Marinacci M, Rustichini A (2012) On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility. J. Math. Econom. 48(6):386–395.Crossref, Google Scholar
• [16] Cui X, Li D, Wang S, Zhu S (2012) Better than dynamic mean-variance: Time inconsistency and free cash flow stream. Math. Finance 22(2):346–378.Crossref, Google Scholar
• [17] Doléans-Dade C (1970) Quelques applications de la formule de changement de variables pour les semimartingales. Z. Wahrscheinlichkeits Verwandte Gebiete 16:181–194.Crossref, Google Scholar
• [18] Eberlein E, Jacod J (1997) On the range of options prices. Finance Stochastics 1(2):131–140.Crossref, Google Scholar
• [19] Émery M (1978) Stabilité des solutions des équations différentielles stochastiques application aux intégrales multiplicatives stochastiques. Z. Wahrscheinlichkeits Verwandte Gebiete 41(3):241–262.Crossref, Google Scholar
• [20] Esche F, Schweizer M (2005) Minimal entropy preserves the Lévy property: How and why. Stochastic Processes Appl. 115(2):299–327.Crossref, Google Scholar
• [21] Filipović D, Kupper M (2007) Monotone and cash-invariant convex functions and hulls. Insurance Math. Econom. 41(1):1–16.Crossref, Google Scholar
• [22] Fujiwara T (2010) The minimal entropy martingale measures for exponential additive processes revisited. J. Math-for-Ind. 2B:115–125. Google Scholar
• [23] Fujiwara T, Miyahara Y (2003) The minimal entropy martingale measures for geometric Lévy processes. Finance Stochastics 7(4):509–531.Crossref, Google Scholar
• [24] Goll T, Rüschendorf L (2001) Minimax and minimal distance martingale measures and their relationship to portfolio optimization. Finance Stochastics 5(4):557–581.Crossref, Google Scholar
• [25] Hodges S (1998) A generalization of the Sharpe Ratio and its application to valuation bounds and risk measures. FORC Preprint 98/88 (April), https://warwick.ac.uk/fac/soc/wbs/subjects/finance/research/wpaperseries/1998/98-88.pdf.Google Scholar
• [26] Hu Y, Shi X, Xu ZQ (2023) Constrained monotone mean-variance problem with random coefficients. SIAM J. Financial Math. 14(3):838–854.Crossref, Google Scholar
• [27] Jacod J, Shiryaev AN (2003) Limit Theorems for Stochastic Processes, Grundlehren der Mathematischen Wissenschaften, 2nd ed., vol. 288 (Springer, Berlin, Heidelberg).Crossref, Google Scholar
• [28] Jakubėnas P (2002) On option pricing in certain incomplete markets. Shiryaev AN, Mishchenko EF, eds. Stochastic Financial Mathematics, Proceedings of the Steklov Institute of Mathematics, vol. 237 (Nauka, Moscow), 123–142.Google Scholar
• [29] Jeanblanc M, Klöppel S, Miyahara Y (2007) Minimal fq-martingale measures of exponential Lévy processes. Ann. Appl. Probab. 17(5–6):1615–1638.Crossref, Google Scholar
• [30] Kallsen J (1999) A utility maximization approach to hedging in incomplete markets. Math. Methods Oper. Res. 50(2):321–338.Crossref, Google Scholar
• [31] Kallsen J (2000) Optimal portfolios for exponential Lévy processes. Math. Methods Oper. Res. 51(3):357–374.Crossref, Google Scholar
• [32] Kallsen J (2004) σ-localization and σ-martingales. Theory Probab. Appl. 48(1):152–163.Crossref, Google Scholar
• [33] Kallsen J, Muhle-Karbe J (2010) Utility maximization in models with conditionally independent increments. Ann. Appl. Probab. 20(6):2162–2177.Crossref, Google Scholar
• [34] Karatzas I, Kardaras C (2007) The numéraire portfolio in semimartingale financial models. Finance Stochastics 11(4):447–493.Crossref, Google Scholar
• [35] Kardaras C (2009) No-free-lunch equivalences for exponential Lévy models under convex constraints on investment. Math. Finance 19(2):161–187.Crossref, Google Scholar
• [36] Li B, Guo J, Tian L (2024) Optimal investment and reinsurance policies for the Cramér–Lundberg risk model under monotone mean–variance preference. Internat. J. Control 97(6):1296–1310.Crossref, Google Scholar
• [37] Li Y, Liang Z, Pang S (2023) Continuous-time monotone mean-variance portfolio selection. Preprint, submitted December 14, https://arxiv.org/abs/2211.12168v3.Google Scholar
• [38] Li Y, Liang Z, Pang S (2025a) Comparison between mean-variance and monotone mean-variance preferences in general markets: A new perspective. Oper. Res. Lett. 61:107298.Crossref, Google Scholar
• [39] Li Y, Liang Z, Pang S (2025b) Comparison between mean-variance and monotone mean-variance preferences under jump diffusion and stochastic factor model. Math. Oper. Res. 50(3):2405–2432.Link, Google Scholar
• [40] Maccheroni F, Marinacci M, Rustichini A (2006) Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74(6):1447–1498.Crossref, Google Scholar
• [41] Maccheroni F, Marinacci M, Rustichini A, Taboga M (2009) Portfolio selection with monotone mean-variance preferences. Math. Finance 19(3):487–521.Crossref, Google Scholar
• [42] Nutz M (2012) Power utility maximization in constrained exponential Lévy models. Math. Finance 22(4):690–709.Crossref, Google Scholar
• [43] Pennanen T, Perkkiö AP (2024) Convex Stochastic Optimization: Dynamic Programming and Duality in Discrete Time, Probability Theory and Stochastic Modelling, vol. 107 (Springer, Cham, Switzerland).Crossref, Google Scholar
• [44] Protter PE (2005) Stochastic Integration and Differential Equations, Stochastic Modelling and Applied Probability, vol. 21 (Springer, Berlin, Heidelberg).Crossref, Google Scholar
• [45] Rockafellar RT (1970) Convex Analysis, Princeton Mathematical Series No. 28 (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• [46] Rockafellar RT, Wets RJB (1998) Variational Analysis, Grundlehren der Mathematischen Wissenschaften, vol. 317 (Springer, Berlin, Heidelberg).Crossref, Google Scholar
• [47] Rudin W (1987) Real and Complex Analysis, 3rd ed. (McGraw-Hill Book Co., New York).Google Scholar
• [48] Schweizer M (1994) Approximating random variables by stochastic integrals. Ann. Probab. 22(3):1536–1575.Crossref, Google Scholar
• [49] Schweizer M (1996) Approximation pricing and the variance-optimal martingale measure. Ann. Probab. 24(1):206–236. Crossref, Google Scholar
• [50] Sharpe WF (1994) The Sharpe ratio. J. Portfolio Management 21(1):49–58.Crossref, Google Scholar
• [51] Shen Y, Zou B (2022) Short communication: Cone-constrained monotone mean-variance portfolio selection under diffusion models. SIAM J. Financial Math. 13(4):SC99–SC112.Crossref, Google Scholar
• [52] Shi X, Xu ZQ (2024) Constrained monotone mean–variance investment-reinsurance under the Cramér-Lundberg model with random coefficients. Systems Control Lett. 188:105796.Crossref, Google Scholar
• [53] Shiryaev AN, Cherny AS (2002) A vector stochastic integral and the fundamental theorem of asset pricing. Proc. Steklov Inst. Math. 237:6–49.Google Scholar
• [54] Strub MS, Li D (2020) A note on monotone mean–variance preferences for continuous processes. Oper. Res. Lett. 48(4):397–400.Crossref, Google Scholar
• [55] Trybuła J, Zawisza D (2019) Continuous-time portfolio choice under monotone mean-variance preferences—Stochastic factor case. Math. Oper. Res. 44(3):966–987.Link, Google Scholar
• [56] Zhitlukhin M (2019) Monotone Sharpe ratios and related measures of investment performance. de Gier J, Praeger C, Tao T, eds. 2017 MATRIX Annals, MATRIX Book Series, vol. 2 (Springer, Cham, Switzerland), 637–665.Crossref, Google Scholar