2007 Fiscal Year Final Research Report Summary
Studies on Modeling of Stock Processes and Its Applications
| Project/Area Number |
16310104
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | Hokkaido University |
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Principal Investigator |
KIMURA Toshikazu Hokkaido University, Graduate School of Economics and Business Administration, Professor (50143649)
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| Co-Investigator(Kenkyū-buntansha) |
INOUE Akihiko Hokkaido University, Graduate School of Science, Associate Professor (50168431)
KOZUMI Hideo Kobe University, Graduate School of Business Administration, Professor (10261273)
SUZUKI Teruyoshi Hokkaido University, Graduate School of Economics and Business Administration, Associate Professor (90360891)
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| Project Period (FY) |
2004 – 2007
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| Keywords | Financial Engineering / Mathematical Finance / Stock Price Processes / Stochastic Models / Path-dependent Options / Portfolio / Market with Memory / Long Memory |
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| Research Abstract |
This paper deals with stochastic and statistical models for stock price processes in financial markets. The purposes are to construct new models in place of the well-known Black-Scholes-Merton model and to apply them to financial problems. During the research period, we obtain the following result:
1. American-style Path-dependent Options: For various path-dependent American options with no explicit solutions, Kimura developed a unifying numerical scheme via the Laplace-Carlson transform, obtaining their values as well as their optimal stopping boundaries. Also, he derived closed-form expressions for the early exercise premiums in the Laplace domain, which have been previously given in complicated integral forms.
2. Financial Markets with Memory: Inoue developed a new model for stock price processes in markets with memory by combining a forecast technique called the past-future method and an innovation process appeared in filtering theory. In his model, we can deal with both short and long memory by adjusting its parameters. In addition, for models with exponential-type memory, he analyzed optimal portfolio selection problems of maximizing a certain utility function.
3. Quantitative Models of Data Observed in Markets: Kozumi developed a multinomial probit model from a Bayesian point of view. Using a prior distribution, he proposed efficient Markov chain Monte Carlo methods, which are examined by both simulated and meal data.
4. Corporate Financial Models: For portfolios including pension, life insurance and property casualty insurance, Suzuki formulated them as optimization problems in the framework of stochastic control theory, and he analyzed them as optimal investment problems in business and household consumption. Through theoretical and numerical examinations, he obtained some properties and economical implications of optimal policies
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Research Products
(169 results)
