Optimization Under Rational Expectations: A Framework of Fully Coupled Forward-Backward Stochastic Linear Quadratic Systems

References

• [1] Antonelli F (1993) Backward-forward stochastic differential equations. Ann. Appl. Probab. 3(3):777–793.Crossref, Google Scholar
• [2] Begg D, Fischer S, Dornbusch R (1989) Economics, 2nd ed. (McGraw-Hill, Maidenhead, UK).Google Scholar
• [3] Bensoussan A (1982) Lectures on stochastic control. Mitter SK, Moro A, eds. Nonlinear Filtering and Stochastic Control (Springer-Verlag, Berlin), 1–62.Crossref, Google Scholar
• [4] Blanchard OJ (1981) Output, the stock market, and interest rates. Amer. Econom. Rev. 71(1):132–143.Google Scholar
• [5] Chen Z, Epstein L (2002) Ambiguity, risk, and asset returns in continuous time. Econometrica 70(4):1403–1443.Crossref, Google Scholar
• [6] Chen S, Zhou XY (2000) Stochastic linear quadratic regulators with indefinite control weight costs. II. SIAM J. Control Optim. 39(4):1065–1081.Crossref, Google Scholar
• [7] Chen S, Li X, Zhou XY (1998) Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim. 36(5):1685–1702.Crossref, Google Scholar
• [8] Cvitanić J, Zhang J (2012) Contract Theory in Continuous-Time Models (Springer Science & Business Media, New York).Google Scholar
• [9] Dokuchaev N, Zhou XY (1999) Stochastic controls with terminal contingent conditions. J. Math. Anal. Appl. 238(1):143–165.Crossref, Google Scholar
• [10] Dornbusch R (1976) Expectations and exchange rate dynamics. J. Political Econom. 84(6):1161–1176.Crossref, Google Scholar
• [11] Duffie D, Epstein LG (1992) Stochastic differential utility. Econometrica 60(2):353–394.Crossref, Google Scholar
• [12] Duffie D, Skiadas C (1994) Continuous-time security pricing: A utility gradient approach. J. Math. Econom. 23(2):107–131.Crossref, Google Scholar
• [13] Duffie D, Geoffard PY, Skiadas C (1994) Efficient and equilibrium allocations with stochastic differential utility. J. Math. Econom. 23(2):133–146.Crossref, Google Scholar
• [14] Duffie D, Ma J, Yong J (1995) Black’s consol rate conjecture. Ann. Appl. Probab. 5(2):356–382.Crossref, Google Scholar
• [15] El Karoui N, Peng S, Quenez MC (1997) Backward stochastic differential equations in finance. Math. Finance 7(1):1–71.Crossref, Google Scholar
• [16] Hu Y, Peng S (1995) Solution of forward-backward stochastic differential equations. Probab. Theory Related Fields 103(2):273–283.Crossref, Google Scholar
• [17] Hu M, Ji S, Xue X (2018) A global stochastic maximum principle for fully coupled forward-backward stochastic systems. SIAM J. Control Optim. 56(6):4309–4335.Crossref, Google Scholar
• [18] Hu M, Ji S, Xue X (2019) Linear quadratic problems for fully coupled forward-backward stochastic control systems. Preprint, submitted February 26, https://doi.org/10.48550/arXiv.1902.09758.Google Scholar
• [19] Huang J, Shi J (2012) Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations. ESAIM Control Optim. Calculus Variations 18(4):1073–1096.Crossref, Google Scholar
• [20] Kartala XI, Englezos N, Yannacopoulos AN (2020) Future expectations modeling, random coefficient forward–backward stochastic differential equations, and stochastic viscosity solutions. Math. Oper. Res. 45(2):403–433.Link, Google Scholar
• [21] Kohlmann M, Tang S (2003) Minimization of risk and linear quadratic optimal control theory. SIAM J. Control Optim. 42(3):1118–1142.Crossref, Google Scholar
• [22] Krugman PR (1991) Target zones and exchange rate dynamics. Quart. J. Econom. 106(3):669–682.Crossref, Google Scholar
• [23] Lim AE, Zhou XY (2001) Linear-quadratic control of backward stochastic differential equations. SIAM J. Control Optim. 40(2):450–474.Crossref, Google Scholar
• [24] Ma J, Yong J (1999) Forward-Backward Stochastic Differential Equations and Their Applications (Springer Science & Business Media, New York).Google Scholar
• [25] Ma J, Protter P, Yong J (1994) Solving forward-backward stochastic differential equations explicitly—A four step scheme. Probab. Theory Related Fields 98(3):339–359.Crossref, Google Scholar
• [26] Ma J, Wu Z, Zhang D, Zhang J (2015) On well-posedness of forward–backward SDEs—A unified approach. Ann. Appl. Probab. 25(4):2168–2214.Crossref, Google Scholar
• [27] Meng Q (2009) A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information. Sci. China Ser. A Math. 52(7):1579–1588.Crossref, Google Scholar
• [28] Miller M, Weller P (1995) Stochastic saddlepoint systems stabilization policy and the stock market. J. Econom. Dynam. Control 19(1–2):279–302.Crossref, Google Scholar
• [29] Neely CJ, Weller PA, Corbae D (1994) Endogenous realignments and the sustainability of a target zone. Working Paper 1994-009D, Federal Reserve Bank of St. Louis, St. Louis.Google Scholar
• [30] Øksendal B, Sulem A (2011) Portfolio optimization under model uncertainty and BSDE games. Quant. Finance 11(11):1665–1674.Crossref, Google Scholar
• [31] Pardoux E, Tang S (1999) Forward-backward stochastic differential equations and quasilinear parabolic PDEs. Probab. Theory Related Fields 114(2):123–150.Crossref, Google Scholar
• [32] Peng S (1993) Backward stochastic differential equations and applications to optimal control. Appl. Math. Optim. 27(2):125–144.Crossref, Google Scholar
• [33] Peng S, Wu Z (1999) Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37(3):825–843.Crossref, Google Scholar
• [34] Summers LH, Bosworth BP, Tobin J, White PM (1981) Taxation and corporate investment: A q-theory approach. Brookings Papers Econom. Activity 1981(1):67–140.Crossref, Google Scholar
• [35] Sun J, Li X, Yong J (2016) Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems. SIAM J. Control Optim. 54(5):2274–2308.Crossref, Google Scholar
• [36] Tang S (2003) General linear quadratic optimal stochastic control problems with random coefficients: Linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42(1):53–75.Crossref, Google Scholar
• [37] Wonham WM (1968) On a matrix Riccati equation of stochastic control. SIAM J. Control 6(4):681–697.Crossref, Google Scholar
• [38] Wu Z (1998) Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems. Systems Sci. Math. Sci. 11(3):249–259.Google Scholar
• [39] Yannacopoulos AN (2008) Rational expectations models: An approach using forward–backward stochastic differential equations. J. Math. Econom. 44(3–4):251–276.Crossref, Google Scholar
• [40] Yong J (1997) Finding adapted solutions of forward–backward stochastic differential equations: Method of continuation. Probab. Theory Related Fields 107(4):537–572.Crossref, Google Scholar
• [41] Yong J (2006) Linear forward-backward stochastic differential equations with random coefficients. Probab. Theory Related Fields 135(1):53–83.Crossref, Google Scholar
• [42] Yong J, Zhou XY (1999) Stochastic Controls: Hamiltonian Systems and HJB Equations (Springer Science & Business Media, New York).Crossref, Google Scholar