Quadratic Hedging and Mean-Variance Portfolio Selection with Random Parameters in an Incomplete Market
Published Online:1 Feb 2004https://doi.org/10.1287/moor.1030.0065
References
- Optimal Control: Linear Quadratic Methods (1989) (Prentice Hall, Englewood Cliffs, NJ) Google Scholar
- Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. (1976) 36:419–414Crossref, Google Scholar
- Stochastic linear quadratic optimal control problems with random coefficients. Chinese Ann. Math. Ser. B (2000) 21:323–338Crossref, Google Scholar
- Optimal consumption and portfolio policies when asset prices follow a diffusion process. J. Econom. Theory (1989) 49:33–83Crossref, Google Scholar
- Convex duality in constrained portfolio optimization. Ann. Appl. Probab. (1992) 2:767–818Crossref, Google Scholar
- The variance-optimal martingale measure for continuous processes. Bernoulli (1996) 2(1):81–105Crossref, Google Scholar
- Optimal hedging and equilibrium in a dynamic futures market. J. Econom. Dynam. Control (1990) 14:21–33Crossref, Google Scholar
- Mean-variance hedging in continuous time. Ann. Appl. Probab. (1991) 1:1–15Crossref, Google Scholar
- Backward stochastic differential equations in finance. Math. Finance (1997) 7:1–71Crossref, Google Scholar
- , Mas-Colell A., Hildenbrand W. Hedging of non-redundant contingent claims. Contributions to Mathematical Economics (1986) (North-Holland, Amsterdam, The Netherlands) 205–233Google Scholar
- Mean-variance hedging and numeraire. Math. Finance (1998) 8(3):179–200Crossref, Google Scholar
- Martingales and stochastic integrals in the theory of continuous trading. Stochastic Proc. Appl. (1981) 20:215–260Crossref, Google Scholar
- A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. (1993) 6:327–343Crossref, Google Scholar
- Indefinite stochastic Riccati equations. SIAM J. Control Optim. (2003) 42:123–137Crossref, Google Scholar
- The pricing of options on assets with stochastic volatilites. J. Finance (1987) 42:281–300Crossref, Google Scholar
- Partial hedging in a stochastic volatility environment. Math. Finance (2002) 12(4):375–409Crossref, Google Scholar
- Methods of Mathematical Finance (1999) (Springer-Verlag, New York) Google Scholar
- Optimal portfolio and consumption decisions for a “small investor” on a finite horizon. SIAM J. Control Optim. (1987) 25:1557–1586Crossref, Google Scholar
- Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. (2000) 28(2):558–602Crossref, Google Scholar
- Optimal control of linear stochastic systems with singular costs, and the mean-variance hedging problem with stochastic market conditions. (2001a) . PreprintGoogle Scholar
- Global adapted solution of linear stochastic systems with singular costs, and the mean-variance hedging problem with stochastic market conditions. (2001b) . PreprintGoogle Scholar
- Global adapted solutions of one-dimensional backward stochastic Riccati equations, with applications to the mean-variance hedging. Stochastic Proc. Appl. (2002) 97:255–258Crossref, Google Scholar
- Relationship between backward stochastic differential equations and stochastic controls: A linear-quadratic approach. SIAM J. Control Optim. (2000) 38:1392–1407Crossref, Google Scholar
- Dynamic programming and mean-variance hedging. Finance Stochastics (1999) 3:83–110Crossref, Google Scholar
- Existence for BSDE with superlinear-quadratic coefficient. Stochastics and Stochastic Rep. (1998) 63:227–240Crossref, Google Scholar
- Optimal dynamic portfolio selection: Multi-period mean-variance formulation. Math. Finance (2000) 10:387–406Crossref, Google Scholar
- , Yin G. G., Zhang Q. Hedging default risk in an incomplete market. Proc. AMS-IMS-SIAM Summer Conf. on Math. of Finance (2003) . ForthcomingGoogle Scholar
- Linear-quadratic control of backward stochastic differential equations: Random parameter case. (2001a) . PreprintGoogle Scholar
- Mean-variance portfolio selection with random parameters in a complete market. Math. Oper. Res. (2001b) 27(1):101–120Link, Google Scholar
- Linear-quadratic control of backward stochastic differential equations. SIAM J. Control Optim. (2001c) 40(2):450–474Crossref, Google Scholar
- Optimization by Vector Space Methods (1968) (John Wiley, New York) Google Scholar
- Portfolio selection. J. Finance (1952) 7:77–91Google Scholar
- Portfolio Selection: Efficient Diversification of Investment (1959) (John Wiley and Sons, New York) Google Scholar
- Adapted solution of backward stochastic equation. Systems Control Lett. (1990) 14:55–61Crossref, Google Scholar
- Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. (1992) 30:284–304Crossref, Google Scholar
- A stochastic calculus model of continuous trading: Optimal portfolios. Math. Oper. Res. (1986) 11:371–382Link, Google Scholar
- Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls. IEEE Trans. Automatic Control (2001) 46(3):428–440Crossref, Google Scholar
- Approximation pricing and the variance-optimal martingale measure. Ann. Probab. (1996) 64:206–236Google Scholar
- Capital asset prices: A theory of market equilibrium under conditions of risk. J. Finance (1964) 19:425–442Google Scholar
- Stock price distributions with stochastic volatility: An analytic approach. Rev. Financial Stud. (1991) 4:727–752Crossref, Google Scholar
- Liquidity preference as behavior toward risk. Rev. Econom. Stud. (1958) 26:65–86Crossref, Google Scholar
- Stochastic Controls: Hamiltonian Systems and HJB Equations (1999) (Springer, New York) Crossref, Google Scholar
- Functional Analysis (1965) (Springer-Verlag, Berlin, Germany) Google Scholar
- Continuous-time mean-variance portfolio selection: A stochastic LQ framework. Appl. Math. Optim. (2000) 42:19–33Crossref, Google Scholar

