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E. SYAHRIL
Bogor Agricultural University
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Mathematics

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PRINSIP MAKSIMUM PONTRYAGIN DALAM MASALAH KONTROL OPTIMUM STOKASTIK E. SYAHRIL
MILANG Journal of Mathematics and Its Applications Vol. 1 No. 2 (2002): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (140.159 KB) | DOI: 10.29244/jmap.1.2.23-36

Abstract

Kontrol Optimum Stokastik merupakan cabang ma- tematika yang relatif baru perkembangannya. Terdapat dua pen- dekatan untuk menentukan solusi masalah kontrol optimum sto- kastik, yaitu prinsip maksimum Pontryagin dan program dinamis Bellman. Tulisan ini menyajikan prinsip maksimum untuk masalah kontrol optimum stokastik dan aplikasinya dalam masalah portofo- lio dan konsumsi. Merton(1971) menyelesaikan masalah konsumsi dan portofolio dengan menggunakan pendekatan program dinamis. Dengan hasil yang diperoleh oleh Merton sebagai patokan, masalah konsumsi dan portofolio diselesaikan dengan pendekatan prinsip maksimum.
AN INVESTMENT STRATEGY IN PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COST E. SYAHRIL
MILANG Journal of Mathematics and Its Applications Vol. 2 No. 2 (2003): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (145.536 KB) | DOI: 10.29244/jmap.2.2.1-14

Abstract

This paper discusses an investment strategy for a con- sumption and investment decision problem for an individual who has available a riskless asset paying fixed interest rate and a risky asset driven by Brownian motion price fluctuations. The individual observes current wealth when making transactions, that transac- tions incur costs, and that decisions to transact can be made at any time based on all current information. The transactions costs is fixed for every transaction, regardless of amount transacted. In addition, the investor is charged a fixed fraction of total wealth as management fee. The investor’s objective is to maximize the expected utility of consumption over a given horizon. The prob- lem faced by the investor is formulated in a stochastic discrete- continuous-time control problem. An investment strategy is given for fixed transaction intervals.
AN OPTIMAL CONTROL FORMULATION OF PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COST E. SYAHRIL
MILANG Journal of Mathematics and Its Applications Vol. 2 No. 1 (2003): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (132.861 KB) | DOI: 10.29244/jmap.2.1.25-36

Abstract

This paper formulates a consumption and investment decision problem for an individual who has available a riskless asset paying fixed interest rate and a risky asset driven by Brownian mo- tion price fluctuations. The individual is supposed to observe his or her current wealth only, when making transactions, that trans- actions incur costs, and that decisions to transact can be made at any time based on all current information. The transactions costs is fixed for every transaction, regardless of amount trans- acted. In addition, the investor is charged a fixed fraction of total wealth as management fee. The investor’s objective is to max- imize the expected utility of consumption over a given horizon. The problem faced by the investor is formulated into a stochastic discrete-continuous-time control problem.
AN OPTIMAL TRANSACTION INTERVALS FOR PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COS E. SYAHRIL
MILANG Journal of Mathematics and Its Applications Vol. 3 No. 1 (2004): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (170.573 KB) | DOI: 10.29244/jmap.3.1.11-26

Abstract

This paper discusses an optimal transaction interval for a consumption and investment decision problem for an indi- vidual who has available a riskless asset paying fixed interest rate and a risky asset driven by Brownian motion price fluctuations. The individual observes current wealth when making transactions, that transactions incur costs, and that decisions to transact can be made at any time based on all current information. The trans- actions costs is fixed for every transaction, regardless of amount transacted. In addition, the investor is charged a fixed fraction of total wealth as management fee. The investor’s objective is to maximize the expected utility of consumption over a given horizon. The problem faced by the investor is formulated in a stochastic discrete-continuous-time control problem. An optimal transaction interval for the inverstor is derived.
PENYELESAIAN MASALAH KONTROL OPTIMUM SEBAGAI MASALAH SYARAT BATAS PERSAMAAN DIFERENSIAL BIASA DALAM SCILAB A. D. GARNADI; E. SYAHRIL
MILANG Journal of Mathematics and Its Applications Vol. 16 No. 2 (2017): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (574.148 KB) | DOI: 10.29244/jmap.16.2.61-76

Abstract

Diuraikan penggunaan rutin bvode di lingkungan SCILAB untuk menyelesaikan masalah syarat batas sistem persamaan diferensial biasa untuk menyelesaikan masalah  kontrol optimum (MKO). Tulisan ini bersifat pedagogis dengan tujuan di mana pengguna dapat mempergunakan solver bvode yang tersedia di lingkungan SCILAB untuk memecahkan masalah syarat batas secara numerik dari  MKO, setelah membaca uraian penggunaan rutin pemecahan masalah syarat batas. Penggunaan rutin digambarkan dengan tiga contoh masalah syarat batas,  salah satu diantaranya berasal dari MKO.
Co-Authors A. D. GARNADI