Abstract—We are concerned with the optimal portfolio problem under stochastic environment; in particular, we deal with the case of two independent stochastic processes in discrete variables. One process is typical random walk, which is regarded as a discrete version of the standard Brownian motion, and the other is the Poisson process. We derive a discrete Hamilton-Jacobi-Bellman (HJB) equation for the value function and try to solve it. Examples are also discussed.
Index Terms—Discrete hamilton-jacobi-bellman equation, discrete processes, multiple stochastic processes, optimal portfolio problem.
Naohiro Yoshida is with the Graduate School of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan (e-mail: ed141003@g.hit-u.ac.jp).
Naoyuki Ishimura is with the Faculty of Commerce, Chuo University, Hachioji, Tokyo 192-0393, Japan (e-mail: naoyuki@tamacc.chuo-u.ac.jp).
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Cite: Naohiro Yoshida and Naoyuki Ishimura, "Remarks on the Optimal Portfolio Problem in Discrete Variables with Multiple Stochastic Processes," International Journal of Modeling and Optimization vol. 6, no. 2, pp. 96-99, 2016.
