Optimal Asset Allocation under Forward Exponential Performance Criteria
Marek Musiela, Thaleia Zariphopoulou
Abstract
This work presents a novel concept in stochastic optimization, namely, the notion of forward performance. As an application, we analyze a portfolio management problem with exponential criteria. Under minimal model assumptions we explicitly construct the forward performance process and the associated optimal wealth and asset allocations. For various model parameters, we recover a range of investment policies that correspond to distinct financial applications.
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1233152948
Digital Object Identifier: doi:10.1214/074921708000000435
References
[1] Fleming, W. H. and Soner, H. M. (2006). Controlled Markov Processes and Viscosity Solutions, second edition. Springer-Verlag.
Mathematical Reviews (MathSciNet):
MR2179357
[2] Kurtz, T. (1984). Martingale problems for controlled processes. In Stochastic Modeling and Filtering (M. Thoma and A. Wyner, eds.) 75–90. Lecture Notes in Control and Information Sciences. Springer-Verlag.
Mathematical Reviews (MathSciNet):
MR894107
Zentralblatt MATH:
0642.93065
Digital Object Identifier: doi:10.1007/BFb0009051
[3] Larson, R. E. (1968). State increment dynamic programming. In Modern Analytic and Computational Methods in Science and Mathematics (R. Bellman, ed.) Elsevier.
Mathematical Reviews (MathSciNet):
MR233583
Zentralblatt MATH:
0204.47101
[4] Musiela, M. and Zariphopoulou, T. (2003). Backward and forward utilities and the associated pricing systems: The case study of the binomial model. Preprint.
[5] Musiela, M. and Zariphopoulou, T. (2008). Derivative pricing, investment management and the term structure of exponential utilities: The single period binomial model. In Indifference Pricing (R. Carmona, ed.) Princeton University Press, in press.
[6] Musiela, M. and Zariphopoulou, T. (2006). Investment and valuation under backward and forward exponential utilities in a stochastic factor model. Dilip Madan’s Festschrift, in press.
[7] Musiela, M. and Zariphopoulou, T. (2006). Investments and forward utilities. Preprint.
[8] Musiela, M., Sokolova, E. and Zariphopoulou, T. (2007). Indifference pricing under forward valuation criteria: The case study of the binomial model. Preprint.
[9] Nisio, M. (1981). Lectures on Stochastic Control Theory. ISI Lecture Notes 9. Macmillan.
Mathematical Reviews (MathSciNet):
MR617741
Zentralblatt MATH:
0453.93056
[10] Penrose, R. (1955). A generalized inverse for matrices. Proceedings of Cambridge Philosophical Society 51 406–413.
Mathematical Reviews (MathSciNet):
MR69793
Digital Object Identifier: doi:10.1017/S0305004100030401
[11] Protter, P. (1990). Stochastic Integration and Differential Equations. Springer-Verlag.
Mathematical Reviews (MathSciNet):
MR1037262
[12] Seinfeld, J. H. and Lapidus, L. (1968). Aspects of the forward dynamic programming algorithm. I&EC Process Design and Development 475–478.
[13] Vit, K. (1977). Forward differential dynamic programming. Journal of Optimization Theory and Applications 21 (4) 487–504.
Mathematical Reviews (MathSciNet):
MR440449
Zentralblatt MATH:
0336.49021
Digital Object Identifier: doi:10.1007/BF00933093
[14] Yong, J. and Zhou, X.-Y. (1999). Stochastic Controls, Hamiltonian Systems and HJB Equations. Springer-Verlag.
Mathematical Reviews (MathSciNet):
MR1696772
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