Source: Ann. Appl. Probab.
Volume 12, Number 4
We consider a general class of optimization problems in financial markets with incomplete information and transaction costs. Under a no-arbitrage condition strictly weaker than the existence of a martingale measure, and when asset prices are quasi-left-continuous processes, we show the existence of optimal strategies. Applications include maximization of expected utility, minimization of coherent risk measures and hedging of contingent claims.
 CVITANI ´C, J. (2000). Minimizing expected loss of hedging in incomplete and constrained markets. SIAM J. Control Optim. 38 1050-1066 (electronic).
 CVITANI ´C, J. and KARATZAS, I. (1996). Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Finance 6 133-165.
 DELBAEN, F. (2000). Coherent risk measures on general probability spaces. Preprint, ETH Zurich.
 DELBAEN, F. and SCHACHERMAy ER, W. (1994). A general version of the fundamental theorem of asset pricing. Math. Ann. 300 463-520.
 DELLACHERIE, C. and MEy ER, P. A. (1978). Probabilities and Potential. North-Holland, Amsterdam.
 DELLACHERIE, C. and MEy ER, P. A. (1982). Probabilities and Potential B. North-Holland, Amsterdam.
 GUASONI, P. (2002). Optimal investment problems under market frictions. Ph.D. thesis, Scuola Normale Superiore, Pisa.
 GUASONI, P. (2002). Risk minimization under transaction costs. Finance and Stochastics 6 91-113.
 JOUINI, E. and KALLAL, H. (1995). Martingales and arbitrage in securities markets with transaction costs. J. Econom. Theory 66 178-197.
 KABANOV, Y. and LAST, G. (2001). Hedging under transaction costs in currency markets: a continuous-time model. Math. Finance 12 63-70.
 KABANOV, Y. M., RÁSONy I, M. and STRICKER, C. (2001). On the closedness of sums of convex cones in l0 and the robust no-arbitrage property. Preprint.
 KABANOV, Y. M. and STRICKER, C. (2001). The Harrison-Pliska arbitrage pricing theorem under transaction costs. J. Math. Econom. 35 185-196.
 KARATZAS, I., LEHOCZKY, J. P., SHREVE, S. E. and XU, G.-L. (1991). Martingale and duality methods for utility maximization in an incomplete market. SIAM J. Control Optim. 29 702-730.
 KRAMKOV, D. O. (1996). Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab. Theory Related Fields 105 459- 479.
 KRAMKOV, D. and SCHACHERMAy ER, W. (1999). The asy mptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9 904-950.
 KREPS, D. M. (1981). Arbitrage and equilibrium in economies with infinitely many commodities. J. Math. Econom. 8 15-35.
 MERTON, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous time case. Rev. Econom. Statist. 51 247-257.
 SCHACHERMAy ER, W. (2001). The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Preprint, TU-Wien.
 SCHACHERMAy ER, W. (2001). Utility maximization in incomplete financial markets. Lecture notes, Scuola Normale Superiore, Pisa.
 YAN, J. A. (1980). Caractérisation d'une classe d'ensembles convexes de L1 ou H 1. Seminar on Probability XIV. Lecture Notes in Math. 784 220-222. Springer, Berlin.
Mathematical Reviews (MathSciNet): MR580127
VIA BUONARROTI, 2 56127 PISA ITALY E-MAIL: email@example.com