"Down-Side Risk" Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates
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Abstract
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.
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Abramowitz M., Stegun I. A. (1970) Handbook of mathematical functions (Ninth printing). Dover Publications Inc, New York
Cox J. C., Ingersol J. E., Ross A. (1985) A theory of term structure of interest rates. Economitrica 53: 385–407
Hall P., Heyde C. C. (1980) Martingale limit theory and its application. Academic Press, New York
Hata H., Nagai H., Sheu S. J. (2010) Asymptotics of the probability minimizing a "Down-side" risk. The Annals of Applied Probability 20(1): 52–89
Hata H., Sekine J. (2006) Solving long term optimal investment problems with Cox-Ingersoll-Ross interest rates. Advances in Mathematics and Economics 8: 231–255
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).
Heston S. (1993) A closed-form solution for stochastic volatility with applications to bond and currency options. Review of Financial Studies 6: 327–343
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.
Nagai, H. (2009). Down-side risk minimization as large deviation control (preprint).
Pham H. (2003) A large deviations approach to optimal long term investment. Finance Stoch 7: 169–195
Revuz D., Yor M. (1999) Continuous martingales and brownian motion (3rd edition). Springer, Berlin
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Hata, H. "Down-Side Risk" Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates. Asia-Pac Financ Markets 18, 69–87 (2011). https://doi.org/10.1007/s10690-010-9121-5
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DOI: https://doi.org/10.1007/s10690-010-9121-5
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