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Measure of Investment Optimal Strategy
Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
- 1 Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
- 2 Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
- 3 Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
- 4 Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
- 5 Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
- 6 Department of Mathematics and Computer Science, Federal University of Petroleum Resources Effurun, Nigeria
Journal of Mathematical Finance·Volume 06 (2016)·Pages 269–274·Published 9 March 2016·DOI10.4236/jmf.2016.62023
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Abstract
In this paper, we considered the different strategies that generate the optimal wealth on investment. The strategy examine depends on the utility function an investor is willing to adopt, say H* at time N in every 2n possible states; in an N period setting. Negative exponential, logarithm, square root and power utility functions were established, as the market structures changed according to a Markov chain through a martingale approach. The problem of maximization is solved via Lagrange method. The performance of the investment from day-to-day is driven by the ratio of the risk neutral probability and the probability of rising to falling.
KeywordsMartingaleNegative ExponentialLogarithmSquare-RootPower Utility Functions
- Battocchio, P. and Menoncin, F. (2004) Optimal Pension Management in a Stochastic Framework. Insurance: Mathematics and Economics, 34, 79-95. http://dx.doi.org/10.1016/j.insmatheco.2003.11.001
- Deelstra, G., Grasselli, M. and Koehl, P.-F. (2003) Optimal Investment Strategies in the Presence of a Minimum Guarantee. Insurance: Mathematics and Economics, 33, 189-207. http://dx.doi.org/10.1016/S0167-6687(03)00153-7
- Deelstra, G., Grasselli, M. and Koehl, P.-F. (2004) Optimal Design of the Guarantee for Defined Contribution Funds. Journal of Economic Dynamics and Control, 28, 2239-2260. http://dx.doi.org/10.1016/j.jedc.2003.10.003
- Delong, L., Gerrard, R. and Haberman, S. (2008) Mean-Variance Optimization Problems for an Accumulation Phase in a Defined Benefit Plan. Insurance: Mathematics and Economics, 42, 107-118. http://dx.doi.org/10.1016/j.insmatheco.2007.01.005
- Emms, P. and Haberman, S. (2007) Asymptotic and Numerical Analysis of the Optimal Investment Strategy for An Insurer. Insurance: Mathematics and Economics, 40 113-134. http://dx.doi.org/10.1016/j.insmatheco.2006.03.003
- Eghwerido, J.T. and Obilade, T.O. (2014) Optimization of Investment Returns with N-Step Utility Functions. Journal of the Nigerian Mathematical Society, 33, 311-320.
- Eghwerido, J.T., Efe-Eyefia, E and Ekuma-Okereke, E (2015) Investment Returns with N-Step Generalized Utility Functions. ICASTOR Journal of Mathematical Sciences, 9, 51-55.
- Hong-Chih, H. (2010) Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model. Journal of Risk and Insurance, 77, 451-472. http://dx.doi.org/10.1111/j.1539-6975.2009.01350.x
- Korn, R. (2005) Worst-Case Scenario Investment for Insurers. Insurance: Mathematics and Economics, 36, 1-11. http://dx.doi.org/10.1016/j.insmatheco.2004.10.004
- Korn, R. and Korn E. (2001) Option Pricing and Portfolio Optimization. AMS, Providence. http://dx.doi.org/10.1007/978-3-322-83210-8
- Korn, R. and Kraft, H. (2003) Optimal Portfolios with Defaultable Securities: A Firms Value Approach. International Journal of Theoretical and Applied Finance, 6, 793-819. http://dx.doi.org/10.1142/S0219024903002213
- Korn, R. and Menkens, O. (2005) Worst-Case Scenario Portfolio Optimization: A New Stochastic Control Approach. Mathematical Methods of Operations Research, 62, 123-140. http://dx.doi.org/10.1007/s00186-005-0444-3