Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

OPTIMAL PORTFOLIO STRATEGIES WITH A LIABILITY AND RANDOM RISK: THE CASE OF DIFFERENT LENDING AND BORROWING RATES

  • Yang, Zhao-Jun (College of Mathematics and Econometrics, Hunan University) ;
  • Huang, Li-Hong (College of Mathematics and Econometrics, Hunan University)
  • 발행 : 2004.05.01

⟨ 이전 논문 다음 논문 ⟩

초록

This paper deals with two problems of optimal portfolio strategies in continuous time. The first one studies the optimal behavior of a firm who is forced to withdraw funds continuously at a fixed rate per unit time. The second one considers a firm that is faced with an uncontrollable stochastic cash flow, or random risk process. We assume the firm's income can be obtained only from the investment in two assets: a risky asset (e.g., stock) and a riskless asset (e.g., bond). Therefore, the firm's wealth follows a stochastic process. When the wealth is lower than certain legal level, the firm goes bankrupt. Thus how to invest is the fundamental problem of the firm in order to avoid bankruptcy. Under the case of different lending and borrowing rates, we obtain the optimal portfolio strategies for some reasonable objective functions that are the piecewise linear functions of the firm's current wealth and present some interesting proofs for the conclusions. The optimal policies are easy to be operated for any relevant investor.

키워드

참고문헌

  1. Math. Oper. Res v.22 Survival and growth with a liability: optimal portfoli o strategies in continuous time S. Browns
  2. Math. Oper. Res. v.20 Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin S. Browne
  3. Math. Oper. Res. v.15 Portfolio selection with transaction costs M. H. A. Davis;A. R. Norman
  4. Math. Oper. Res. v.16 An optimal investment-consumption model with borrowing W. H. Fleming;T. Zariphopoulou
  5. A Second Course on Stochastic Process S. Karlin and H. M. Taylor
  6. Controlled Diffusion Process N. V. Krylov
  7. Ph. D. Thesis, Central South University Problems on Options, Investment and Consumption Z. J. Yang
  8. Chinese J. of Applied Probability and Statistics v.16 An explicit solution to optimal investment and consumption with partial information Z. J. Yang;Z. Z. Li;J. Z. Zou
  9. Int. J. of Theoretical and Applied Finance v.4 Optimal trading strategy with partial information and the value of information: the simplified and generalized models Z. J. Yang;C. Q. Ma
  10. J. of Applied Mathematics for China Universities v.9 no.A Optimal investment and consumption strategies Z. J. Yang;Y. M. Shi
  11. J. AppI. Math. & Computing(old KJCAM) v.8 Oscillations of certain nonliean delay parabolic boundary value problems L. Q. Zhang;X. L. Fu
  12. J. Appi. Math. & Computing(old KJCAM) v.8 Oscillatory behavior of the second-order nonlinear neutral difference equations Z. G. Zhang;W. L. Dong;B. Ping