Optimal investment and consumption models with non-linear stock dynamics

Mathematical Methods of Operations Research

Volumn 50, Issue 2, 1999, Pages 271-296

  Zariphopoulou, Thaleia ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Closed form solutions; Constrained viscosity solutions; Hamilton Jacobi Bellman equation; Portfolio management

Indexed keywords

EID: 0010590593     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001860050098     Document Type: Article

References (39)

1. Barles G, Burdeau J, Romano M, Samsoen N (1993) Estimation de frontière libre des options américaines au voisinage de l'échéance. Comptes Rendus des Séances de l'Académie des Sciences. Série I, Mathématique (Paris) 316:171-174
2. Barles G, Soner HM (1998) Option pricing with transaction costs and a non-linear Black and Scholes equation. Finance and Stochastics 2:369-398
3. Capuzzo-Dolcetta I, Lions P-L (1990) Hamilton-Jacobi equations with state constraints. Transactions of the American Mathematical Society 318:543-683
4. Constantinides G, Zariphopoulou T (1999a) Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences. Finance and Stochastics 3:345-369
5. Constantinides G, Zariphopoulou T (1999b) Bounds on derivative prices in an intertemporal setting with proportional transaction costs and multiple securities, submitted for publication
6. Crandall M, Ishii H, Lions P-L (1992) User's guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society 27:1-67
7. Crandall M, Lions P-L (1983) Viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society 277:1-42
8. Cvitanic J, Karatzas I (1995) On portfolio optimization under "drawdown" constraints. Mathematical Finance, Springer Verlag, New York, pp. 35-46
9. Davis MHA, Panas VG, Zariphopoulou T (1993) European option pricing with transaction costs. SIAM Journal of Control and Optimization 31:470-493
10. Duffie D, Fleming WH, Soner HM, Zariphopoulou T (1997) Hedging in incomplete markets with HARA utility. Journal of Economic Dynamics and Control 21:753-782
11. Duffie D, Zariphopoulou T (1993) Optimal investment with undiversifiable income risk. Mathematical Finance 3:135-148
12. Evans LC, Souganidis P (1984) Differential games and representation formulas for solutions of Hamiltonian-Jacobi-Isaacs equations. Indiana University Mathematics Journal 33:773-797
13. Fitzpatrick B, Fleming WH (1990) Numerical methods for optimal investment-consumption models. In: Proceedings of the IEEE Conference on Decision and Control
14. Fleming WH, Soner HM (1993) Controlled Markov processes and viscosity solutions. Springer Verlag, New York
15. Fleming WH, Souganidis P (1989) On the existence of value functions of two player, zero sum stochastic differential games. Indiana University Mathematics Journal 38:293-314
16. Fleming WH, Zariphopoulou T (1991) An optimal investment and consumption models with borrowing constraints. Mathematics of Operations Research 16:802-822
17. Freidlin M (1985) Functional integration and partial differential equations. Princeton University Press, Princeton, NJ
18. Gikhman I, Skorohod A (1972) Stochastic differential equations. New York: Springer-Verlag
19. Huang C-F, Pagès H (1992) Optimal consumption and portfolio policies in an infinite horizon: existence and convergence. Annals of Applied Probability 2:36-64
20. Ishii H, Lions P-L (1990) Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Journal of Differential Equations 83:26-78
21. Karatzas I, Lehoczky JP, Sethi SP, Shreve SE (1986) Explicit solution of a general consumption/investment problem. Mathematics of Operations Research 11:261-294
22. Karatzas I, Lehoczky JP, Shreve SE (1987) Optimal portfolio and consumption decisions for a "small investor" on a finite horizon. SIAM Journal on Control and Optimization 25:1157-1586
23. Karatzas I, Lehoczky JP, Shreve SE, Xu GL (1991) Martingale and duality methods for utility maximization in an incomplete market. SIAM Journal on Control and Optimization 29:702-730
24. Krylov N (1980) Controlled diffusion processes. Springer-Verlag, New York
25. Lions P-L (1983) Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. 1: The dynamic programming principle and applications; 2: Viscosity solutions and uniqueness. Communications in Partial Differential Equations 8:1101-1174, 1229-1276
26. Merton RC (1969) Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics 51:247-257
27. Merton RC (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3:373-413; erratum, Journal of Economic Theory 6:213-214 (1973)
28. Pichler A (1996) On transaction costs and HJB equations. Preprint
29. Scheinkman J, Zariphopoulou T (1999) Optimal environmental management in the presence of irreversibilities. Journal of Economic Theory, in press
30. Shreve SE, Soner HM (1994) Optimal investment and consumption with transaction costs. Annals of Applied Probability 4:609-692
31. Soner HM (1986) Optimal control with state space constraints. SIAM Journal on Control and Optimization 24:552-562, 1110-1122
32. Tourin A, Zariphopoulou T (1994) Numerical schemes for investment models with singular transactions. Computational Economics 7:287-307
33. Young V, Zariphopoulou T (1999) Stochastic variational formulae for distorted probabilities. Insurance: Mathematics and Economics, to appear
34. Zariphopoulou T (1989) Optimal investment/consumption models with constraints. Doctoral dissertation, Division of Applied Mathematics, Brown University, Providence, RI
35. Zariphopoulou T (1992) Investment-consumption models with transaction fees and Markov-chain parameters. SIAM Journal on Control and Optimization 30:613-636
36. Zariphopoulou T (1994) Consumption investment models with constraints. SIAM Journal of Control and Optimization 32:59-84
37. Zariphopoulou T (1999a) Closed form solutions for valuation models with unhedgeable risks. submitted for publication
38. Zariphopoulou T (1999b) Reaction-diffusion equations in market equilibria with unhedgeable risks, working paper
39. Zariphopoulou T (1999c) Valuation with unhedgeable risks with jump diffusion processes: closed form solutions, working paper