The foreign exchange market modeled as a nonlinear-hyperbolic stochastic differential game : a study in the operation of financial markets.

Kam, Simon W (1997). The foreign exchange market modeled as a nonlinear-hyperbolic stochastic differential game : a study in the operation of financial markets. PhD Thesis, School of Economics, The University of Queensland.

       
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Author Kam, Simon W
Thesis Title The foreign exchange market modeled as a nonlinear-hyperbolic stochastic differential game : a study in the operation of financial markets.
School, Centre or Institute School of Economics
Institution The University of Queensland
Publication date 1997
Thesis type PhD Thesis
Supervisor Professor Clem Tisdell
Professor Kevin Burrage
Total pages 392
Language eng
Subjects 0102 Applied Mathematics
140103 Mathematical Economics
1401 Economic Theory
Formatted abstract
Consider a foreign exchange market with two kinds of representative agents — those who have knowledge of the market "fundamentals" of the exchange rate (named information traders or "fundamentalists"), and those who do not (named noise traders or "chartists"). For the lack of better knowledge, noise traders base their forecasts upon historical trends, and expect the exchange rate to follow an Ornstein-Uhlenbeck process. Information traders, however, have knowledge of the "fundamental" exchange rate, and expect the traded exchange rate to move toward the "fundamental" rate. Given these two exchange rate "forecasting" processes, expressed in two stochastic nonlinear differential equations, both type of traders attempt to maximize their expected (stochastic) Hyperbolic-Absolutely-Risk-Averse (HARA) utility functions by controlling their respective portfolio, consumption and importation choices. This nonlinear-hyperbolic stochastic differential game can be solved by carrying out proper Girsanov transformations, more widely known in the derivatives pricing literature as the method of "risk-neutral" valuation. As expected, the optimal portfolio plays for both types of agents do not involve their risk preferences, which is consistent with the application of the risk-neutral valuation approach to the problem. The realized exchange rate, the outcome of the stochastic differential game, has to be jointly determined by the two types of agents, and it no longer follows the geometric Brownian motion process. Numerical simulations show that the realized exchange rate fluctuates around but does not deviate too much from the exchange rate determined by the fundamental factors. Also, the model is stable, that is the realized exchange rates and players' wealth remain bounded, over a wide range of parameter values.
Keyword Foreign exchange market -- Mathematical models.
Additional Notes

Variant title: Foreign exchange stochastic differential game

Document type: Thesis
Collection: UQ Theses (RHD) - UQ staff and students only
 
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Created: Tue, 07 Dec 2010, 15:25:57 EST by Mrs Jennifer Creese on behalf of Social Sciences and Humanities Library Service