scholarly journals AN INVESTMENT STRATEGY IN PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COST

2003 ◽  
Vol 2 (2) ◽  
pp. 1
Author(s):  
E. SYAHRIL
Keyword(s):  
Brownian Motion ◽  
Continuous Time ◽  
Decision Problem ◽  
Investment Decision ◽  
Investment Strategy ◽  
Transactions Costs ◽  
Time Control ◽  
The Individual ◽  
Riskless Asset ◽  
Total Wealth

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.

scholarly journals AN OPTIMAL TRANSACTION INTERVALS FOR PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COS

2004 ◽  
Vol 3 (1) ◽  
pp. 11
Author(s):  
E. SYAHRIL
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Decision Problem ◽  
Investment Decision ◽  
Time Control ◽  
The Individual ◽  
Riskless Asset ◽  
Total Wealth

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.

scholarly journals AN OPTIMAL CONTROL FORMULATION OF PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COST

2003 ◽  
Vol 2 (1) ◽  
pp. 25
Author(s):  
E. SYAHRIL
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Continuous Time ◽  
Decision Problem ◽  
Investment Decision ◽  
Transactions Costs ◽  
Time Control ◽  
The Individual ◽  
Riskless Asset ◽  
Total Wealth

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.

scholarly journals An Optimal Transaction Intervals for Portfolio Selection Problem with Bullet Transaction Cost

2017 ◽  
Author(s):  
SYAHRIL
Keyword(s):  
Interest Rate ◽  
Control Problem ◽  
Transaction Cost ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Investment Decision ◽  
Risky Asset ◽  
Selection Problem ◽  
Transactions Costs ◽  
Time Control

This paper discusses an optimal transaction interval for a consumption and investment decision problemfor an~individual who has available a~risklessasset paying fixed interest rate and a~risky asset driven byBrownian 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 transactions costs is fixed for every transaction, regardless of amount transacted. In addition, the investor is charged a fixed fraction oftotal wealth as management fee. The investor's objective is to maximize the expectedutility 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.

MINIMIZING THE PROBABILITY OF LIFETIME RUIN: TWO RISKLESS ASSETS WITH TRANSACTION COSTS

2019 ◽  
Vol 49 (03) ◽  
pp. 847-883
Author(s):  
Xiaoqing Liang ◽  
Virginia R. Young
Keyword(s):  
Transaction Costs ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Money Market ◽  
The Other ◽  
Proportional Transaction Costs ◽  
Optimal Investment Strategy ◽  
The Individual ◽  
Riskless Asset

AbstractWe compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds are subject to proportional transaction costs. We consider the following three cases. (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

scholarly journals Optimal Investment Strategy for Risky Assets

1998 ◽  
Vol 01 (03) ◽  
pp. 377-387 ◽  
Author(s):  
Sergei Maslov ◽  
Yi-Cheng Zhang
Keyword(s):  
Growth Rate ◽  
Brownian Motion ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Assets ◽  
Average Return ◽  
Optimal Investment Strategy

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and volatility of an asset are relevant indicators determining its optimal weight. Our results are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.

scholarly journals A Contribution on Stochastic Optimal Control to Quantitative Finance

2018 ◽  
Author(s):  
SYAHRIL
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Nonlinear Equation ◽  
Stochastic Optimal Control ◽  
Investment Decision ◽  
Optimal Solution ◽  
Investment Strategies ◽  
Transactions Costs ◽  
Quantitative Finance ◽  
Total Wealth

This work considers a consumption and investment decision problemfor an~individual who has available a~risklessasset paying fixed interest rate and a~risky asset driven byBrownian motion price fluctuations.The individual is supposed to observe his orher current wealth only, when making transactions, that transactions incur costs,and that decisions to transact can be made at any time based on all current information.The transactions costs under consideration could be a fixed, linear or a nonlinear functionof the amount transacted. In addition, the investor is charged a fixed fraction oftotal wealth as management fee. The investor's objective is to maximize the expectedutility of consumption over a given horizon.On the basis of this model, the existence of an optimal solution is given.Optimal consumption and investment strategies are obtained in closed formfor each type of transaction costs function.In addition, the optimalinterval of time between transactions is also derived.Results show that, for each transaction cost, transaction interval satisfies a nonlinear equation,which depends on total wealth at the beginning of that intervals.If, at each tran-saction, there is no costs involved other than that of management feewhich is a fixed fraction of current portfolio value, then the optimalinterval of time between transactions is fixed, independent of time and currentwealth.

Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

2008 ◽  
Vol 38 (01) ◽  
pp. 231-257 ◽  
Author(s):  
Holger Kraft ◽  
Mogens Steffensen
Keyword(s):  
Continuous Time ◽  
Optimal Solution ◽  
Decision Problems ◽  
Optimal Consumption ◽  
Continuous Time Markov Chain ◽  
Financial Decision Making ◽  
Markov Chain Approach ◽  
Special Cases ◽  
Financial Decision ◽  
The Individual

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

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