Optimal Investment Rule in an Inefficient Financial Market

2005 ◽  
Author(s):  
Yaping Wang ◽  
Yunhong Yang ◽  
Chunsheng Zhou
Keyword(s):  
Financial Market ◽  
Optimal Investment

scholarly journals Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 1012-1026
Author(s):  
Sahar Albosaily ◽  
Serguei Pergamenchtchikov
Keyword(s):  
Financial Markets ◽  
Numerical Simulations ◽  
Financial Market ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Dynamical Programming ◽  
Verification Theorem ◽  
Logarithmic Utility ◽  
Hamilton Jacobi Bellman ◽  
Optimal Investment And Consumption

We consider a spread financial market defined by the multidimensional Ornstein–Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions using a stochastic dynamical programming method. We show a special verification theorem for this case. We find the solution to the Hamilton–Jacobi–Bellman (HJB) equation in explicit form and as a consequence we construct optimal financial strategies. Moreover, we study the constructed strategies with numerical simulations.

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 Malliavin method for optimal investment in financial markets with memory

2016 ◽  
Vol 14 (1) ◽  
pp. 286-299 ◽  
Author(s):  
Qiguang An ◽  
Guoqing Zhao ◽  
Gaofeng Zong
Keyword(s):  
Financial Market ◽  
Mean Field ◽  
Optimal Investment ◽  
Volterra Equations ◽  
Necessary Condition ◽  
Dynamic Programming Method ◽  
Classical Dynamic ◽  
Stochastic Volterra Equation ◽  
Optimal Investment Problem ◽  
With Memory

AbstractWe consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market. We show a sufficient and necessary condition for the optimal investment in this financial market with memory by mean-field stochastic maximum principle.

scholarly journals Dynamic Index Optimal Investment Strategy Based on Stochastic Differential Equations in Financial Market Options

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Financial Market ◽  
Capital Investment ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Insurance Companies ◽  
Investment Efficiency ◽  
Bank Deposits ◽  
Optimal Investment Strategy

With the gradual development and improvement of the financial market, financial derivatives such as futures and options have also become the objects of competition in the financial market. Therefore, how to make the most favorable and optimized investment and consumption when options are included? It has become a problem facing investors. Aiming at the optimal investment problem of investors, this paper studies the calculation of an optimal investment strategy in stochastic differential equations in financial market options on the basis of fuzzy theory. Now, stochastic calculus has become an important branch of stochastic analysis, finance, control, and other fields. The study of introducing stochastic differential equations is mainly to solve the stochastic control problem, which is the principle of the stochastic maximum. In finance, some hedging or pricing problems of contingent rights can eventually be transformed into a series of stochastic differential equations. Based on the historical data of five aspects of bank deposits, bonds, funds, stocks, and real estate of four listed insurance companies, the paper analyzes the optimization strategy of the capital investment of listed insurance companies based on the investment yield of the domestic investment market. According to the final results, the historical proportion of bank deposits of the superior company is 27%, and the optimal proportion given by the model is 25%; the total proportion of funds and stocks is 15%, and the optimal proportion of funds analyzed in the model is 20% and the optimal proportion of stocks is 10%. Therefore, the final results show that the investment efficiency of listed insurance companies can actually increase investment in stocks and funds and reduce the proportion of bank deposits to obtain greater investment returns.

Worst-Case Investment Strategy with Delay

2018 ◽  
Vol 6 (1) ◽  
pp. 35-57
Author(s):  
Chunxiang A ◽  
Yi Shao
Keyword(s):  
Financial Market ◽  
Normal State ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Model Parameters ◽  
Investment Strategies ◽  
Case Scenario ◽  
Worst Case ◽  
Risky Assets ◽  
Investment Optimization

AbstractThis paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.

scholarly journals A Modified Markowitz Multi-Period Dynamic Portfolio Selection Model Based on the LDIW-PSO

2015 ◽  
Vol 8 (1) ◽  
pp. 90 ◽  
Author(s):  
Shuai Shao ◽  
Li-qun Yang ◽  
Yuan-biao Zhang ◽  
Zhi-hui Meng
Keyword(s):  
Financial Market ◽  
Optimal Investment ◽  
Capital Allocation ◽  
Sharpe Ratio ◽  
Estimation Errors ◽  
Portfolio Returns ◽  
Real Risk ◽  
Study Results ◽  
Capital Allocation Efficiency ◽  
Dynamic Portfolio

<p>Modern financial market is an extremely complicated nonlinear system, while gaming and speculation in the market makes the returns and risks of financial assets a great deal of uncertainty. How to construct an effective portfolio, realize the maximization of portfolio returns and the minimization of risks, and optimize the investment capital allocation efficiency are becoming increasingly a hot topic. This paper discusses a revised Markowitz Multi-period Dynamic portfolio mode by introducing LDIW-PSO in the process of solving the optimal investment weight. The LDIW-PSO has greatly improved the efficiency of searching the optimal weight of the portfolio. In addition, this paper introduces exponential-revised Sharpe ratio (Ex-Sharpe) as the objective function and adopts the optimal variance bound to reflect the real risk preferences of the investors in the financial markets better and modify covariance estimation errors of Mean-Variance model. The empirical study results show that the LDIW-PSO is very suitable for solving the dynamic portfolio model, and the exponential-revised Sharpe ratio can reflect financial market investment situation accurately and avoid covariance errors effectively.</p>

scholarly journals Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Peng Yang
Keyword(s):  
Probability Measure ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Control Technique ◽  
Model Parameters ◽  
Cev Model ◽  
Terminal Wealth ◽  
Optimal Investment Strategy

A robust time-consistent optimal investment strategy selection problem under inflation influence is investigated in this article. The investor may invest his wealth in a financial market, with the aim of increasing wealth. The financial market includes one risk-free asset, one risky asset, and one inflation-indexed bond. The price process of the risky asset is governed by a constant elasticity of variance (CEV) model. The investor is ambiguity-averse; he doubts about the model setting under the original probability measure. To dispel this concern, he seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. The objective of the investor is to seek a time-consistent strategy so as to maximize his expected terminal wealth meanwhile minimizing his variance of the terminal wealth in the worst-case scenario. By using the stochastic optimal control technique, we derive closed-form solutions for the optimal time-consistent investment strategy, the probability scenario, and the value function. Finally, the influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments.

scholarly journals Computation of optimal investment allocations in a sequential portfolio optimisation

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Masiala Mavungu ◽  
Evan Hurwitz ◽  
Tshilidzi Marwala
Keyword(s):  
Risk Management ◽  
Mathematical Models ◽  
Financial Market ◽  
Financial Risk ◽  
Risk Measure ◽  
Optimal Investment ◽  
Portfolio Optimisation ◽  
Computational Simulations ◽  
Financial Risk Management ◽  
Linearly Constrained

Orientation: This article is related to Financial Risk Management, Investment Management and Portfolio Optimisation.Research purpose: The aim is to compute optimal investment allocations from one period to another.Motivation of the study: Financial market systems are governed by random behaviours expressing the complexity of the economy and the politics. Risk Measure and Management are current and major issues for financial market operators and attract the attention of researchers who develop suitable tools and methods to describe and control risk. In this article, financial risk management is considered for an investor operating in the financial market.Research approach/design and method: This research developed Mathematical Models to describe the problem and Computational Simulations to compute, summarise the results and show their reliabilities.Main findings: The results are the investments allocations stored, some tables and the related computational simulations. By going from period one to another, one can notice from the graphs that the portfolio risk is decreasing and the portfolio profit increasing.Practical/managerial implications: The approach used in this article shows a way of solving rigorously any linearly constrained quadratic optimisation problem and any constrained nonlinear problem. It gives the ability of transforming judiciously certain linearly constrained nonlinear programming problems into sequences of linearly constrained quadratic problems and solving them efficiently.Contributions/value-add: This article developed Mathematical Models and Matlab Computer Optimisation Programs to give Computational Simulations. It wrote Computer Programs for a fifth-order autoregressive model to forecast asset profits.

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