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Warianty tytułu
Języki publikacji
Abstrakty
We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
547--560
Opis fizyczny
Bibliogr. 14 poz., wykr.
Twórcy
autor
- Cracow University of Economics Department of Mathematics Rakowicka 27, 31-510 Kraków, Poland
Bibliografia
- [1] I. Ekeland, E. Taflin, A theory of bond portfolios, Ann. Appl. Probab. 15 (2005), 1260-1305.
- [2] W.H. Fleming, T. Pang, An application of stochastic control theory to financial economics, SIAM J. Control Optim. 43 (2004), 502-531.
- [3] W.H. Fleming, H.M. Soner, Controlled Markov Processes and Viscosity Solutions, 2nd Edition, Springer, New York, 2006.
- [4] H. Hata, S. Sheu, On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: I. Existence of solution, SIAM J. Control Optim. 50 (2012), 2373-2400.
- [5] H. Hata, S. Sheu, On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: II. Verification theorem, SIAM J. Control Optim. 50 (2012), 2401-2430.
- [6] R. Korn, H. Kraft, A stochastic control approach to portfolio problems with stochastic interest rates, SIAM J. Control Optim. 40 (2001), 1250-1269.
- [7] R.C. Merton, Optimal consumption and portfolio rules in continuous time, J. Econom. Theory 3 (1971), 373-413.
- [8] B. 0ksendal, A. Sulem, Applied Stochastic Control of Jump Diffusions, Springer-Verlag, Berlin, 2005.
- [9] T. Pang, Stochastic portfolio optimization with log utility, Int. J. Theor. Appl. Finance 9 (2006), 869-887.
- [10] H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Springer-Verlag, Berlin, Heidelberg, 2009.
- [11] N. Ringer, M. Teheranchi, Optimal portfolio choice in the bond market, Finance Stoch. 10 (2006), 553-573.
- [12] D. Synowiec, Problem inwestora na rynku obligacji, PhD Thesis, AGH, Kraków, 2011, http://winntbg.bg.agh.edu.pl/rozprawy2/10 321/fulllO 321.pdf.
- [13] D. Synowiec, Optimal consumption problem in a diffusion short-rate model, arXiv: 0910.0378.
- [14] T. Zariphopoulou, Optimal asset allocation in stochastic factor model - an overview and open problems, Advanced Financial Modelling, Radon Series Comp. Appl. Math. 8 (2009), 427-453.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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