Computational Economics

, Volume 39, Issue 2, pp 195–217 | Cite as

Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information

  • Jinqiang Yang
  • Zhaojun Yang


This paper extends real options theory to consider the situation where the mean appreciation rate of the value of an irreversible investment project is not observable and governed by an Ornstein–Uhlenbeck process. Our main purpose is to analyze the impact of the uncertainty of the mean appreciation rate on the pricing and investment timing of the option to invest under incomplete markets with partial information. We assume that an investor aims to maximize expected discounted utility of lifetime consumption. Based on consumption utility indifference pricing method, stochastic control and filtering theory, we obtain under CARA utility the implied values and the optimal investment thresholds of the option to invest, which are determined by a semi-closed-form solution to a free-boundary partial differential equation (PDE) problem. The solution is independent of the utility time-discount rate. We provide numerical results by finite difference methods and compare the results with those under a fully observable case. Numerical calculations show that partial information leads to a significant loss of the implied value of the option to invest. This loss, called implied information value, IIV increases quickly with the uncertainty of the mean appreciation rate. A high volatility of project values might decrease the IIV, as well as the implied value of the option.


Partial information Consumption utility-based indifference pricing Real options Implied information value 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Borison A. (2005) Real options analysis: Where are the emperor’s clothes?. Journal of Applied Corporate Finance 17: 17–31CrossRefGoogle Scholar
  2. Brennan M. J. (1998) The role of learning in dynamic portfolio decisions. European Economic Review 1: 295–305Google Scholar
  3. Décamps J. P., Mariotti T., Villeneuve S. (2005) Investment timing under incomplete information. Mathematics of Operations Research 30(2): 472–500CrossRefGoogle Scholar
  4. Dixit A., Pindyck R. (1994) Investment under uncertainty. Princeton University Press, Princeton, NJGoogle Scholar
  5. Ewald C., Yang Z. J. (2008) Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward tdiosyncratic risk. Mathematical Methods of Operations Research 68(1): 97–123CrossRefGoogle Scholar
  6. Fleming W. H., Soner H. M. (2006) Controlled Markov processes and viscosity solutions. Springer, New York, NYGoogle Scholar
  7. Gennotte G. (1986) Optimal portfolio choice under incomplete information. Journal of Finance 41(3): 733–746CrossRefGoogle Scholar
  8. Henderson V. (2002) Valuation of claims on non-tradable asset using utility maximization. Mathematical Finance 12(4): 351–373CrossRefGoogle Scholar
  9. Henderson V. (2007) Valuing the option to invest in an incomplete market. Mathematics and Financial Economics 7(1): 103–128CrossRefGoogle Scholar
  10. Henderson V., Hobson D. (2002) Real options with constant relative risk aversion. Journal of Economic Dynamics and Control 27(2): 329–355CrossRefGoogle Scholar
  11. Klein, M. (2007). Irreversible investment under incomplete information. Working Paper, INSEAD.Google Scholar
  12. Klein M. (2009) Comment on “investment timing under incomplete information”. Mathematics of Operations Research 34(2): 249–254CrossRefGoogle Scholar
  13. Krylov N. V. (1980) Controlled diffusion process. Springer, New York, NYGoogle Scholar
  14. Lakner P. (1998) Optimal trading strategy for an investor: The case of partial information. Stochastic Process and their Applications 76: 77–97CrossRefGoogle Scholar
  15. Liptser R. S., Shiryayev A. N. (1977) Statistics of random processes. Springer-Verlag, New York, NYGoogle Scholar
  16. McDonald R., Siegel D. (1986) The value of waiting to invest. Quarterly Journal of Economics 101: 707–727CrossRefGoogle Scholar
  17. Merton R. C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3(4): 373–414CrossRefGoogle Scholar
  18. Merton R. (1980) On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics 8: 323–362CrossRefGoogle Scholar
  19. Miao J. J., Wang N. (2007) Investment, consumption, and hedging under incomplete markets. Journal of Financial Economics 86(3): 608–642CrossRefGoogle Scholar
  20. Monoyios M. (2007) Optimal hedging an parameter uncertainty. IMA Journal of Management Mathematics 18: 331–351CrossRefGoogle Scholar
  21. Monoyios, M. (2008). Marginal utility-based hedging of claims on non-traded assets with partial information (Preprint).Google Scholar
  22. Myers S. C. (1977) Determinants of corporate borrowing. Journal of Financial Economics 5(2): 147–176CrossRefGoogle Scholar
  23. Myers S. C., Majd S. (1990) Abandonment value and project life. Advances in Futures and Options Research 4: 1–21Google Scholar
  24. Pham H. (2005) On some recent aspects of stochastic control and their applications. Probability Surveys 2: 506–549CrossRefGoogle Scholar
  25. Pham H. (2009) Continuous-time stochastic control and optimization with financial applications. Springer-Verlag, BerlinCrossRefGoogle Scholar
  26. Rouge R., El Karoui N. (2000) Pricing via utility maximization and entropy. Mathematical Finance 10(2): 259–276CrossRefGoogle Scholar
  27. Xiong J., Zhou X. Y. (2007) Mean-variance portfolio selection under partial information. SIAM Journal on Control and Optimization 46: 156–175CrossRefGoogle Scholar
  28. Yang Z. J., Ma C. Q. (2001) Optimal trading strategy with partial information and the value of information: the simplified and generalized models. International Journal of Theoretical and Applied Finance 4(5): 759–772CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.School of Finance and StatisticsHunan UniversityChangshaPeople’s Republic of China

Personalised recommendations