Hostname: page-component-cb9f654ff-r5d9c Total loading time: 0 Render date: 2025-08-19T13:31:25.114Z Has data issue: false hasContentIssue false
  • English
  • Français

Ordering of Optimal Portfolio Allocations in a Model with a Mixture of Fundamental Risks

Part of: Distribution theory - Probability Applications

Published online by Cambridge University Press:  14 July 2016

Ka Chun Cheung  and
Hailiang Yang
Ka Chun Cheung*
Affiliation:
University of Calgary
Hailiang Yang*
Affiliation:
The University of Hong Kong
*
∗ Postal address: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T3A 2E2, Canada. Email address: kccheung@math.ucalgary.ca
∗∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study a single-period optimal portfolio problem in which the aim of the investor is to maximize the expected utility. We assume that the return of every security in the market is a mixture of some common underlying source of risks. A sufficient condition to order the optimal allocations is obtained, and it is shown that several models studied in the literature before are special cases of the proposed model. In the course of the analysis concepts in stochastic orders are employed, and a new characterization of the likelihood ratio order is obtained.

Keywords

Asset allocationstochastic orderdependence structurecomonotonicityweak convergencelikelihood ratio order

MSC classification

Secondary: 62P05: Applications to actuarial sciences and financial mathematics 60E15: Inequalities; stochastic orderings

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 55 - 66
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.Google Scholar
[2] Cheung, K. C. (2006). Optimal portfolio problem with unknown dependency structure. Insurance Math. Econom. 38, 167–175.Google Scholar
[3] Cheung, K. C. (2007). Optimal allocation of policy limits and deductibles. Insurance Math. Econom. 41, 382–391.Google Scholar
[4] Cheung, K. C. and Yang, H. (2004). Ordering optimal proportions in the asset allocation problem with dependent default risks. Insurance Math. Econom. 35, 595–609.Google Scholar
[5] Dhaene, J. et al. (2002). The concept of comonotonicity in actuarial science and finance: theory. Insurance Math. Econom. 31, 3–33.Google Scholar
[6] Föllmer, H. and Schied, A. (2004). Stochastic Finance. An Introduction in Discrete Time (De Gruyter Studies Math. 27). Walter de Gruyter, Berlin.Google Scholar
[7] Hennessy, D. A. and Lapan, H. E. (2002). The use of Archimedean copulas to model portfolio allocations. Math. Finance 12, 143–154.Google Scholar
[8] Hoffmann-Jørgensen, J. (1973). Existence of measurable modifications of stochastic processes. Z. Wahrscheinlichkeitsth. 25, 205–207.Google Scholar
[9] Kijima, M. and Ohnishi, M. (1996). Portfolio selection problems via the bivariate characterization of stochastic dominance relations. Math. Finance 6, 237–277.Google Scholar
[10] Lapan, H. E. and Hennessy, D. A. (2002). Symmetry and order in the portfolio allocation problem. Econom. Theory 19, 747–772.Google Scholar
[11] Shaked, M. and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.Google Scholar
[12] Stroock, D. W. (1993). Probability Theory, An Analytic View. Cambridge University Press.Google Scholar