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A multiobjective approach for weapon selection and planning problems in dynamic environments
A real option approach for investment opportunity valuation
1.  School of Management and Economics, University of Electronic Science and Technology, Chengdu, China 
2.  College of Economics and Management, Zhejiang University of Technology, China 
3.  Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 
4.  Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, Australia 
In this paper, the valuation of an investment opportunity in a hightech corporation using real option theory and modern capital budgeting is studied. Some key characteristics such as highrisk, multistage and technology life cycle of a hightech project are considered in the proposed model. Since a real option is usually not tradable in the market, an actuarial approach is adopted in our study. We employ an irreversible regimeswitching Markov chain to model the multistage and technology life cycle of the project in the hightech industry. The valuation of captured real option can be formulated as the valuation of an American option with timedependent strike price. For the purpose of practical implementation, a novel latticebased method is developed to value the American option. Numerical examples are given to illustrate the proposed models and methods.
References:
[1] 
C. Alexander and X. Chen, A general approach to real option valuation with application to real estate investments, University of Reading, ICMA Centre Discussion Paper No. DP201204. Available at SSRN: http://ssrn.com/abstract=1990957.Google Scholar 
[2] 
N. Bollen, Valuing option in regimeswitching models, Journal of Derivatives, 6 (1998), 3849. Google Scholar 
[3] 
N. Bollen, Real options and product life cycles, Management Science, 45 (1999), 670684. Google Scholar 
[4] 
R. A. Brealey and S. C. Myers, Principles of Corporate Finance, McGrawHill, New York, 1992.Google Scholar 
[5] 
P. P. Boyle and Y. Tian, An explicit finite difference approach to the pricing of barrier options, Applied Mathematical Finance, 5 (1988), 1743. Google Scholar 
[6] 
P. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, Journal of Finance, 47 (1992), 271293. Google Scholar 
[7] 
P. P. Boyle, Option valuation using a threejump process, International Options Journal, 3 (1986), 712. Google Scholar 
[8] 
P. P. Boyle, A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23 (1988), 112. Google Scholar 
[9] 
J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7 (1979), 229263. Google Scholar 
[10] 
M. G. Colombo, A. Croce and S. Murtinu, Ownership structure, horizontal agency costs and the performance of hightech entrepreneurial firms, Small Business Economics, 42 (2014), 265282. Google Scholar 
[11] 
R. E. Caves, Industrial organization and new findings in the turnover and mobility of firms, Journal of Economic Literature, 36 (1998), 19471982. Google Scholar 
[12] 
D. L. Deeds, D. DeCarolis and J. Coombs, Dynamic capabilities and new product development in high technology ventures: an empirical analysis of new biotechnology firms, Journal of Business Venturing, 15 (2000), 211229. Google Scholar 
[13] 
P. A. Geroski, What do we know about entry?, International Journal of Industrial Organization, 13 (1995), 450456. Google Scholar 
[14] 
X. Huang, N. Song, W. K. Ching, T. K. Siu and C. K. Yiu, A real option approach to optimal inventory management of retail products, Journal of Industrial and Management Optimization, 8 (2012), 379389. doi: 10.3934/jimo.2012.8.379. Google Scholar 
[15] 
B. Kamrad and P. Ritchken, Multinomial approximating models for options with $k$ state variables, Management Science, 37 (1991), 16401652. Google Scholar 
[16] 
D. Kellogg and J. M. Charnes, Realoptions valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 7684. Google Scholar 
[17] 
F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation: a simple leastsquares approach, The Review of Financial Studies, 14 (2001), 113147. Google Scholar 
[18] 
J. Mun, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, 2006.Google Scholar 
[19] 
S. C. Myers, Finance theory and financial strategy, Interfaces, 14 (1984), 126137. Google Scholar 
[20] 
V. K. Narayanan, Managing Technology and Innovation for Competitive Advantage, Englewood Cliffs, NJ: Prentice Hall, 2001.Google Scholar 
[21] 
S. Ruhrmann, J. Hochdörffer and G. Lanza, A methodological approach to evaluate supplier development based on real options, Production Engineering, 8 (2014), 373382. Google Scholar 
[22] 
E. S. Schwartz and M. Moon, Rational pricing of Internet companies, Financial Analysts Journal, 56 (2000), 6275. Google Scholar 
[23] 
E. S. Schwartz and M. Moon, Rational pricing of Internet companies revisited, The Financial Review, 36 (2001), 726. Google Scholar 
[24] 
J. E. Smith and R. F. Nau, Valuing risky projects option pricing theory and decision analysis, Management Science, 41 (1995), 795816. Google Scholar 
[25] 
J. E. Smith and K. F. McCardle, Valuing oil properties: Integrating option pricing and decision analysis approaches, Operations Research, 46 (1998), 198217. Google Scholar 
[26] 
J. Sutton, Gibrat's legacy, Journal of Economic Literature, 35 (1997), 4059. Google Scholar 
[27] 
F. M. Tseng, Y. J. Chiu and J. S. Chen, Measuring business performance in the hightech manufacturing industry: A case study of Taiwan's largesized TFTLCD panel companies, Omega, 37 (2009), 686697. Google Scholar 
[28] 
L. Trigeorgis and S. P. Mason, Valuing managerial flexibility, Midland Corporate Finance Journal, 5 (1987), 1421. Google Scholar 
[29] 
L. Trigeorgis and S. Ioulianou, Valuing a hightech growth company: The case of EchoStar communications corporation, The European Journal of Finance, 19 (2013), 734759. doi: 10.1080/1351847X.2011.640343. Google Scholar 
[30] 
B. M. West and J. Bengtsson, Aggregate production process design in global manufacturing using a real options approach, International Journal of Production Research, 45 (2013), 17451762. Google Scholar 
[31] 
D. D. Wu and D. L. Olson, Computational simulation and risk analysis: An introduction of state of the art research, Mathematical and Computer Modelling, 58 (2013), 15811587. doi: 10.1016/j.mcm.2013.07.004. Google Scholar 
[32] 
D. D. Wu, D. L. Olson and J. R. Birge, Introduction to special issue on" Enterprise risk management in operations", Internatonal Journal of Production Economics, 134 (2011), 12. Google Scholar 
[33] 
D. D. Wu, O. Baron and O. Berman, Bargaining in competing supply chains with uncertainty, European Journal of Operational Research, 197 (2009), 548556. doi: 10.1016/j.ejor.2008.06.032. Google Scholar 
[34] 
E. Wang, T. Su, D. Tsai and C. Lin, Fuzzy multiplegoal programming for analyzing outsourcing costeffectiveness in hitech manufacturing, International Journal of Production Research, 51 (2013), 39203944. Google Scholar 
[35] 
L. Wu and F. Liou, A quantitative model for ERP investment decision: Considering revenue and costs under uncertainty, International Journal of Production Research, 49 (2011), 67136728. Google Scholar 
[36] 
L. Y. Wu, Entrepreneurial resources, dynamic capabilities and startup performance of Taiwan's hightech firms, Journal of Business research, 60 (2007), 549555. Google Scholar 
[37] 
Z. X. Wang and Y. Y. Wang, Evaluation of the provincial competitiveness of the Chinese hightech industry using an improved TOPSIS method, Expert Systems with Applications, 41 (2014), 28242831. Google Scholar 
[38] 
F. Yuen and H. Yang, Option pricing in a jumpdiffusion model with regime switching, Astin Bulletin, 39 (2009), 515539. doi: 10.2143/AST.39.2.2044646. Google Scholar 
[39] 
L. Zhu, A simulation based real options approach for the investment evaluation of nuclear power, Computers & Industrial Engineering, 63 (2012), 585593. Google Scholar 
show all references
References:
[1] 
C. Alexander and X. Chen, A general approach to real option valuation with application to real estate investments, University of Reading, ICMA Centre Discussion Paper No. DP201204. Available at SSRN: http://ssrn.com/abstract=1990957.Google Scholar 
[2] 
N. Bollen, Valuing option in regimeswitching models, Journal of Derivatives, 6 (1998), 3849. Google Scholar 
[3] 
N. Bollen, Real options and product life cycles, Management Science, 45 (1999), 670684. Google Scholar 
[4] 
R. A. Brealey and S. C. Myers, Principles of Corporate Finance, McGrawHill, New York, 1992.Google Scholar 
[5] 
P. P. Boyle and Y. Tian, An explicit finite difference approach to the pricing of barrier options, Applied Mathematical Finance, 5 (1988), 1743. Google Scholar 
[6] 
P. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, Journal of Finance, 47 (1992), 271293. Google Scholar 
[7] 
P. P. Boyle, Option valuation using a threejump process, International Options Journal, 3 (1986), 712. Google Scholar 
[8] 
P. P. Boyle, A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23 (1988), 112. Google Scholar 
[9] 
J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7 (1979), 229263. Google Scholar 
[10] 
M. G. Colombo, A. Croce and S. Murtinu, Ownership structure, horizontal agency costs and the performance of hightech entrepreneurial firms, Small Business Economics, 42 (2014), 265282. Google Scholar 
[11] 
R. E. Caves, Industrial organization and new findings in the turnover and mobility of firms, Journal of Economic Literature, 36 (1998), 19471982. Google Scholar 
[12] 
D. L. Deeds, D. DeCarolis and J. Coombs, Dynamic capabilities and new product development in high technology ventures: an empirical analysis of new biotechnology firms, Journal of Business Venturing, 15 (2000), 211229. Google Scholar 
[13] 
P. A. Geroski, What do we know about entry?, International Journal of Industrial Organization, 13 (1995), 450456. Google Scholar 
[14] 
X. Huang, N. Song, W. K. Ching, T. K. Siu and C. K. Yiu, A real option approach to optimal inventory management of retail products, Journal of Industrial and Management Optimization, 8 (2012), 379389. doi: 10.3934/jimo.2012.8.379. Google Scholar 
[15] 
B. Kamrad and P. Ritchken, Multinomial approximating models for options with $k$ state variables, Management Science, 37 (1991), 16401652. Google Scholar 
[16] 
D. Kellogg and J. M. Charnes, Realoptions valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 7684. Google Scholar 
[17] 
F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation: a simple leastsquares approach, The Review of Financial Studies, 14 (2001), 113147. Google Scholar 
[18] 
J. Mun, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, 2006.Google Scholar 
[19] 
S. C. Myers, Finance theory and financial strategy, Interfaces, 14 (1984), 126137. Google Scholar 
[20] 
V. K. Narayanan, Managing Technology and Innovation for Competitive Advantage, Englewood Cliffs, NJ: Prentice Hall, 2001.Google Scholar 
[21] 
S. Ruhrmann, J. Hochdörffer and G. Lanza, A methodological approach to evaluate supplier development based on real options, Production Engineering, 8 (2014), 373382. Google Scholar 
[22] 
E. S. Schwartz and M. Moon, Rational pricing of Internet companies, Financial Analysts Journal, 56 (2000), 6275. Google Scholar 
[23] 
E. S. Schwartz and M. Moon, Rational pricing of Internet companies revisited, The Financial Review, 36 (2001), 726. Google Scholar 
[24] 
J. E. Smith and R. F. Nau, Valuing risky projects option pricing theory and decision analysis, Management Science, 41 (1995), 795816. Google Scholar 
[25] 
J. E. Smith and K. F. McCardle, Valuing oil properties: Integrating option pricing and decision analysis approaches, Operations Research, 46 (1998), 198217. Google Scholar 
[26] 
J. Sutton, Gibrat's legacy, Journal of Economic Literature, 35 (1997), 4059. Google Scholar 
[27] 
F. M. Tseng, Y. J. Chiu and J. S. Chen, Measuring business performance in the hightech manufacturing industry: A case study of Taiwan's largesized TFTLCD panel companies, Omega, 37 (2009), 686697. Google Scholar 
[28] 
L. Trigeorgis and S. P. Mason, Valuing managerial flexibility, Midland Corporate Finance Journal, 5 (1987), 1421. Google Scholar 
[29] 
L. Trigeorgis and S. Ioulianou, Valuing a hightech growth company: The case of EchoStar communications corporation, The European Journal of Finance, 19 (2013), 734759. doi: 10.1080/1351847X.2011.640343. Google Scholar 
[30] 
B. M. West and J. Bengtsson, Aggregate production process design in global manufacturing using a real options approach, International Journal of Production Research, 45 (2013), 17451762. Google Scholar 
[31] 
D. D. Wu and D. L. Olson, Computational simulation and risk analysis: An introduction of state of the art research, Mathematical and Computer Modelling, 58 (2013), 15811587. doi: 10.1016/j.mcm.2013.07.004. Google Scholar 
[32] 
D. D. Wu, D. L. Olson and J. R. Birge, Introduction to special issue on" Enterprise risk management in operations", Internatonal Journal of Production Economics, 134 (2011), 12. Google Scholar 
[33] 
D. D. Wu, O. Baron and O. Berman, Bargaining in competing supply chains with uncertainty, European Journal of Operational Research, 197 (2009), 548556. doi: 10.1016/j.ejor.2008.06.032. Google Scholar 
[34] 
E. Wang, T. Su, D. Tsai and C. Lin, Fuzzy multiplegoal programming for analyzing outsourcing costeffectiveness in hitech manufacturing, International Journal of Production Research, 51 (2013), 39203944. Google Scholar 
[35] 
L. Wu and F. Liou, A quantitative model for ERP investment decision: Considering revenue and costs under uncertainty, International Journal of Production Research, 49 (2011), 67136728. Google Scholar 
[36] 
L. Y. Wu, Entrepreneurial resources, dynamic capabilities and startup performance of Taiwan's hightech firms, Journal of Business research, 60 (2007), 549555. Google Scholar 
[37] 
Z. X. Wang and Y. Y. Wang, Evaluation of the provincial competitiveness of the Chinese hightech industry using an improved TOPSIS method, Expert Systems with Applications, 41 (2014), 28242831. Google Scholar 
[38] 
F. Yuen and H. Yang, Option pricing in a jumpdiffusion model with regime switching, Astin Bulletin, 39 (2009), 515539. doi: 10.2143/AST.39.2.2044646. Google Scholar 
[39] 
L. Zhu, A simulation based real options approach for the investment evaluation of nuclear power, Computers & Industrial Engineering, 63 (2012), 585593. Google Scholar 
        
8  0.38  0.3  0.2  0.2  0.4  0.3  0.0012  0.85  0.6 
        
8  0.38  0.3  0.2  0.2  0.4  0.3  0.0012  0.85  0.6 
Case 1  Case 2  Case 3  Case 4  
Time  
Time  Fixed time  Any time  Any time  Any time 
Probability of  1 if  Uniform rate  Concave function  Convex function 
 0 if  
( 
Case 1  Case 2  Case 3  Case 4  
Time  
Time  Fixed time  Any time  Any time  Any time 
Probability of  1 if  Uniform rate  Concave function  Convex function 
 0 if  
( 
Combination of Stages 2 and 3  (1, 5)  (2, 4)  (3, 3)  (4, 2)  (5, 1) 
Option Value  4.08  6.09  8.25  10.40  12.30 
Combination of Stages 2 and 3  (1, 5)  (2, 4)  (3, 3)  (4, 2)  (5, 1) 
Option Value  4.08  6.09  8.25  10.40  12.30 
Case of  Case 1  Case 2  Case 3  Case 4 
Option Value  8.25  8.22  8.91  9.78 
Case of  Case 1  Case 2  Case 3  Case 4 
Option Value  8.25  8.22  8.91  9.78 
Combination of Stages 2 and 3  (1, 5)  (2, 4)  (3, 3)  (4, 2)  (5, 1) 
Option Value  5.25  7.26  9.41  11.56  13.47 
Combination of Stages 2 and 3  (1, 5)  (2, 4)  (3, 3)  (4, 2)  (5, 1) 
Option Value  5.25  7.26  9.41  11.56  13.47 
Case of  Case 1  Case 2  Case 3  Case 4 
Option Value  9.41  8.99  9.70  10.61 
Case of  Case 1  Case 2  Case 3  Case 4 
Option Value  9.41  8.99  9.70  10.61 
Invest  Divest  
Path 1  Path 2  Path 3  Path 4  Path 1  Path 2  Path 3  Path 4  
r=0.0001  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.0012  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.0023  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
1γ= 0.2  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.5  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.8      t=3    t=4  t=5  t=8  t=6 
p_{12} = 0.04  t=2  t=2  t=2  t=2  t=8  t=8  t=8  t=8 
0.44  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.84  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
μ_{q}^{2}= 0.05  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.2  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.35  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
K_{in}=0.1  t=2  t=2  t=2  t=2  
2.1  t=1  t=1  t=1  t=1  
4.1  t=1  t=1  t=1  t=1  
K_{di}=2.5  t=5  t=5  t=5  t=5  
0.5  t=8  t=8  t=8  t=8  
1.5  t=8  t=8  t=8  t=8 
Invest  Divest  
Path 1  Path 2  Path 3  Path 4  Path 1  Path 2  Path 3  Path 4  
r=0.0001  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.0012  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.0023  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
1γ= 0.2  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.5  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.8      t=3    t=4  t=5  t=8  t=6 
p_{12} = 0.04  t=2  t=2  t=2  t=2  t=8  t=8  t=8  t=8 
0.44  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.84  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
μ_{q}^{2}= 0.05  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.2  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
0.35  t=1  t=1  t=1  t=1  t=8  t=8  t=8  t=8 
K_{in}=0.1  t=2  t=2  t=2  t=2  
2.1  t=1  t=1  t=1  t=1  
4.1  t=1  t=1  t=1  t=1  
K_{di}=2.5  t=5  t=5  t=5  t=5  
0.5  t=8  t=8  t=8  t=8  
1.5  t=8  t=8  t=8  t=8 
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