“Down-Side Risk” Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates
- 97 Downloads
With a bank account and a risky stock, both of which are affected by Cox-Ingersoll-Ross’s interest rates, we treat two “down-side risk” minimization problems of the large deviation probability for long-term investment. Explicit solutions of the problems are given by solving the associated risk-sensitive portfolio optimization problems.
KeywordsLarge deviations control Risk-sensitive stochastic control Bellman equation Long-term investment CIR-interest rates Bessel process with linear drift
Unable to display preview. Download preview PDF.
- Abramowitz M., Stegun I. A. (1970) Handbook of mathematical functions (Ninth printing). Dover Publications Inc, New YorkGoogle Scholar
- Hall P., Heyde C. C. (1980) Martingale limit theory and its application. Academic Press, New YorkGoogle Scholar
- Hata, H., & Sekine, J. (2010). Explicit solution to a certain non-ELQG risk-sensitive stochastic control problem, to appear. Applied Mathematical Optimization. doi: 10.1007/s00245-010-9106-9.
- Hata, H., & Sheu, S. J. (2009). “Down-side risk” probability minimization problem for a multidimensional model with stochastic volatility (preprint).Google Scholar
- Kaise, H., & Sheu, S. J. (2005). Evaluation of large time expectations for diffusion processes. http://www.math.sinica.edu.tw/www/people/websty1.jsp?owner=sheusj.
- Nagai, H. (2010). Asymptotics of probability minimizing a “down-side” risk under partial information, to appear. Quantitative Finance.Google Scholar
- Nagai, H. (2009). Down-side risk minimization as large deviation control (preprint).Google Scholar
- Revuz D., Yor M. (1999) Continuous martingales and brownian motion (3rd edition). Springer, BerlinGoogle Scholar