Bounds for Goal Achieving Probabilities of Mean-Variance Strategies with a No Bankruptcy Constraint

Affiliation(s)

Department of Applied Mathematics, University of Western Ontario, London, Canada.

Department of Mathematics, Université du Québec à Montréal, Montreal, Canada.

Department of Applied Mathematics, University of Western Ontario, London, Canada.

Department of Mathematics, Université du Québec à Montréal, Montreal, Canada.

ABSTRACT

We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance financial investment strategy under a non-negative wealth restriction.

Cite this paper

A. Scott and F. Watier, "Bounds for Goal Achieving Probabilities of Mean-Variance Strategies with a No Bankruptcy Constraint,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 2022-2025. doi: 10.4236/am.2012.312A278.

A. Scott and F. Watier, "Bounds for Goal Achieving Probabilities of Mean-Variance Strategies with a No Bankruptcy Constraint,"

References

[1] X. Li and X. Y. Zhou, “Continuous-Time Mean-Variance Efficiency: The 80% Rule,” Annals of Applied Probability, Vol. 16, No. 4, 2006, pp. 1751-1763. doi:10.1214/105051606000000349

[2] A. Scott and F. Watier, “Goal Achieving Probabilities of Constrained Mean-Variance Strategies,” Statistics & Probability Letters, Vol. 81, No. 8, 2011, pp. 1021-1026. doi: 10.1016/j.spl.2011.02.023

[3] T. R. Bielecki, H. Jin, S. R. Pliska and X. Y. Zhou, “Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition,” Mathematical Finance, Vol. 15, No. 2, 2005, pp. 213-244. doi:10.1111/j.0960-1627.2005.00218.x

[4] E. Di Nardo, A. G. Nobile, E. Pirozzi and L. M. Ricciardi, “A Computational Approach to First-Passage-Time Problems for Gauss-Markov Processes,” Advances in Applied Probability, Vol. 33, No. 2, 2001, pp. 453-482. doi:10.1239/aap/999188324

[5] M. Lopez and G. Still, “Semi-Infinite Programming,” European Journal of Operational Research, Vol. 180, No. 2, 2007, pp. 491-518. doi:10.1016/j.ejor.2006.08.045

[6] R. Reemtsen and J.-J. Rückmann, “Semi-Infinite Programming,” Kluwer Academic Publishers, The Netherlands, 1998.

[1] X. Li and X. Y. Zhou, “Continuous-Time Mean-Variance Efficiency: The 80% Rule,” Annals of Applied Probability, Vol. 16, No. 4, 2006, pp. 1751-1763. doi:10.1214/105051606000000349

[2] A. Scott and F. Watier, “Goal Achieving Probabilities of Constrained Mean-Variance Strategies,” Statistics & Probability Letters, Vol. 81, No. 8, 2011, pp. 1021-1026. doi: 10.1016/j.spl.2011.02.023

[3] T. R. Bielecki, H. Jin, S. R. Pliska and X. Y. Zhou, “Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition,” Mathematical Finance, Vol. 15, No. 2, 2005, pp. 213-244. doi:10.1111/j.0960-1627.2005.00218.x

[4] E. Di Nardo, A. G. Nobile, E. Pirozzi and L. M. Ricciardi, “A Computational Approach to First-Passage-Time Problems for Gauss-Markov Processes,” Advances in Applied Probability, Vol. 33, No. 2, 2001, pp. 453-482. doi:10.1239/aap/999188324

[5] M. Lopez and G. Still, “Semi-Infinite Programming,” European Journal of Operational Research, Vol. 180, No. 2, 2007, pp. 491-518. doi:10.1016/j.ejor.2006.08.045

[6] R. Reemtsen and J.-J. Rückmann, “Semi-Infinite Programming,” Kluwer Academic Publishers, The Netherlands, 1998.