Abstract
This paper addresses the problem of dynamic asset allocation under a bounded shortfall risk in a market composed of three assets: cash, stocks and a zero coupon bond. The dynamics of the instantaneous short rates is driven by a Hull and White model. In this setting, we determine and compare optimal investment strategies maximizing the CRRA utility of terminal wealth with and without value at risk constraint.
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Artzner, P., Delbaen, F., Eber, J., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.
Basak, S. (1995). A general equilibrium model of portfolio insurance. Review of Financial Studies, 8, 1059–1090.
Basak, S., & Shapiro, A. (2001). Value-at-risk-based risk management: optimal policies and asset prices. Review of Financial Studies, 14, 371–405.
Brigo, D., & Mercurio, F. (2006). Springer finance: Interest rate models—theory and practice.
Cairns, A. (1998). Descriptive bond-yield and forward-rate models for the British government securities market. British Actuarial Journal, 4, 265–321.
Cairns, A. (2004). Interest rate models, an introduction. Princeton: Princeton University Press.
Dana, R. A., & Jeanblanc, M. (2002). Springer finance: Financial markets in continuous time.
Deelstra, G., Grasselli, M., & Khoel, P. F. (2003). Optimal investment strategies in presence of a minimum guarantee. Insururance: Mathematics and Economics, 33, 189–207.
Emmer, S., Klüppelberg, C., & Korn, R. (2000). Optimal portfolios with bounded downside risks (Technical report). Munich University of Technology. Available at www-m4.ma.tum.de/papers.
Emmer, S., Klüppelberg, C., & Korn, R. (2001). Optimal portfolios with bounded capital-at-risk. Mathematical Finance, 11, 365–385.
Gabih, A., Grecksch, W., & Wunderlich, R. (2005). Dynamic portfolio optimization with bounded shortfall risks. Stochasic Analysis and Applications, 3, 579–594.
Gandy, R. (2005). Portfolio optimization with risk constraints. PhD thesis, University of Ulm. Available at http://vts.uni-ulm.de/docs/2005/5427/vts_5427.pdf.
Hull, J., & White, A. (1990). Pricing interest rate derivative securities. Review of Financial Studies, 3, 573–592.
Hull, J. C. (1997). Options, futures and other derivatives (3rd ed.). Englewood Cliffs: Prentice-Hall.
Karatzas, I. (1989). Optimization problems in the theory of continuous trading. SIAM Journal of Control and Optimization, 27, 1221–1259.
Karatzas, I., Lehoczky, J. P., & Schreve, S. (1987). Optimal portfolio and consumption decisions for a small investor on a finite horizon. SIAM Journal of Control and Optimization, 25, 1557–1586.
Korn, R., & Kraft, H. (2001). A stochastic control approach to portfolio problems with stochastic interest rates. SIAM Journal of Control and Optimization, 40, 1250–1269.
Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous time case. Review of Economics and Statistics, 51, 247–257.
Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory, 3, 373–413.
Musiela, M., & Rutkowski, M. (1997). Springer finance: Martingale methods in financial modelling.
Shreve, S. (2004). Springer finance: Stochastic calculus for finance II: Continuous time models.
Sørensen, C. (1999). Dynamic asset allocation and fixed income management. Journal of Financial and Quantitative Analysis, 34, 513–531.
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Hainaut, D. Dynamic asset allocation under VaR constraint with stochastic interest rates. Ann Oper Res 172, 97–117 (2009). https://doi.org/10.1007/s10479-008-0509-9
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DOI: https://doi.org/10.1007/s10479-008-0509-9