An Optimal Investment Returns with N-Step Utility Functions

Eghwerido, Joseph Thomas; Obilade, Titilola

doi:10.18052/www.scipress.com/BMSA.16.96

BMSA > BMSA Volume 16 > An Optimal Investment Returns with N-Step Utility...

< Back to Volume

An Optimal Investment Returns with N-Step Utility Functions

Full Text PDF

Abstract:

In this paper, we shall validate the optimal payoff of an investment with an N-step utility function, [6, 7], such that H* is the payoff at time N in every possible state say 2n; in an N period market setting. Negative exponential, logarithm, square root and power utility functions were considered as the market structures change according to a Markov chain. These models were used to predict the performances of some selected companies in the Nigeria Capital Market. The estimates for models design parameters p, q, p', q' correspond to halving or doubling of investment. The performance of any utility function is determined by the ratio q: q' of the probability of rising to falling as well as the ratio p: p' of the risk neutral probability measure of rising to the falling.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 16)

Pages:

96-104

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.16.96

Citation:

J. T. Eghwerido and T. Obilade, "An Optimal Investment Returns with N-Step Utility Functions", Bulletin of Mathematical Sciences and Applications, Vol. 16, pp. 96-104, 2016

Online since:

August 2016

Authors:

Joseph Thomas Eghwerido, Titilola Obilade

Keywords:

Capital Market, Investment Performances, Market Setting, Neutral Probability, Utility Functions

Export:

RIS, BibTeX, Text

Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] P. Battocchio, and F. Menoncin, Optimal Pension Management in a Stochastic Framework, Insurance: Mathematics and Economics, 34, 79-95, (2004).

[2] G. Deelstra, M. Grasselli, and P. -F. Koehl, Optimal Investment Strategies in the Presence of a Minimum Guarantee, Insurance: Mathematics and Economics, 33, 189-207, (2003).

[3] G. Deelstra, M. Grasselli, and P. -F. Koehl, Optimal Design of the Guarantee for Defined Contribution Funds, Journal of Economic Dynamics and Control, 28, 2239-2260, (2004).

[4] L. Delong, R. Gerrard, and S. Haberman, MeanVariance Optimization Problems for an Accumulation Phase in a Defined Benefit Plan, Insurance: Mathematics and Economics, 42, 107-118, (2008).

[5] P. Emms, and S. Haberman, Asymptotic and Numerical Analysis of the Optimal Investment Strategy for An Insurer, Insurance: Mathematics an Economics, 40, 113-134, (2007).

[6] J. T. Eghwerido and T. O. Obilade, Optimization of Investment Returns with N- Step Utility Functions, Journal of the Nigerian Mathematical Society 33, 311-320, (2014).

[7] J. T. Eghwerido, E Efe-Eyefia, and E Ekuma-Okereke, Investment Returns with N- Step Generalized Utility Functions, ICASTOR Journal of Mathematical Sciences 9(2), 51-55, (2015).

[8] H. Hong-Chih Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model, Journal of Risk and Insurance, 77(2), 451-472, (2010).

[9] R. Korn, Worst-case scenario investment for insurers. Insur Math Econ 36, 1-11, (2005).

[10] R. Korn, and E. Korn, Option pricing and portfolio optimization. AMS, Providence, (2001).

[11] R. Korn and H. Kraft, Optimal portfolios with defaultable securities: a firms value approach. Int J Theory Appl Financ 6 793-819, (2003).

[12] R. Korn and O. Menkens, Worst-case scenario portfolio optimization: a new sto- chastic control approach. Math Methods Oper Res 62 (1) 123-140, (2005).

[13] H. Kraft and M. Steffensen, Portfolio problems stopping at first hitting time with application to default risk. Math Methods Oper Res 63, 123-150, (2006).

[14] Louis Bachelier's 'Theory of Speculation published by Princeton Press 1990, (1964).

[15] MacDonald, B. -J., an A. J.G. Cairns, Getting Feedback on Defined Contribution Pension Plans, Journal of Risk and Insurance, 76(2), 385-417, (2009).

[16] Markowitz H., Portfolio selection, Journal of Finance 7, 77-91, 19, (2005).

[17] H. Martin, Martingale pricing applied to Dynamic Portfolio Optimization and Real Options, International Journal of Theoretical and Applied Finance, Vol 11, Issue (2005).

[18] J. Mulvey and B. Shetty, Financial Planning via Multi-Stage Stochastic Optimiza- tion, Computers and Operations Research, 31(1), 1-20, (2004).

[19] Oshorne The Econometric Modelling of Financial Time Series, Second Edition Terence Mills, http: /www. cambridge. org.

[20] H. Pham, On some recent aspects of stochastic control and their applications, Probability Surveys 2 506-549, (2005).

[21] L.C.G. Rogers, The relaxed investor and parameter uncertainty Finance Stochastic 5, 131-154, (2001).

[22] W. Schachermayer, Utility maximization in incomplete markets, In: Stochastic methods in finance, Lectures given at the CIME-EMS Summer in Bressanone/Brixen, Italy, (M. Fritelli, W. Runggladier, eds. ), Springer Lecture notes in Mathematics, 1856, (2003).

[23] M. Schweizer, A guided tour through quadratic hedging approaches, in option pricing interest rates, and risk management, eds. Jouini E., Museiela M., Cvitanic J., Cambridge university Press, 538-574, (2001).

[24] Von-Neumann and Morgenstern Theory of games and economic behavior, Princeton University Press.

Show More Hide

Cited By:

This article has no citations.