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.

Optimal Investment Rule in an Inefficient Financial Market

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

IRREVERSIBLE INVESTMENT, OPERATING FLEXIBILITY, AND TIME LAGS

2010 ◽  
Vol 27 (02) ◽  
pp. 271-286 ◽  
Author(s):  
RYUTA TAKASHIMA ◽  
MAKOTO GOTO ◽  
MOTOH TSUJIMURA
Keyword(s):  
Time Lag ◽  
Peak Load ◽  
Price Volatility ◽  
Optimal Investment ◽  
Capacity Expansion ◽  
Fixed Cost ◽  
Time Lags ◽  
Investment Timing ◽  
Power Company ◽  
Optimal Investment Problem

We consider an optimal investment problem when a firm such as an electric power company has the operational flexibility to expand and contract capacity with fixed cost. This problem is formulated as an impulse control problem combined with optimal stopping. Consequently, we obtain optimal investment timing, optimal capacity expansion and contraction timing, and the investment value. We also show investment, capacity expansion and contraction rule are influenced by the price volatility and the initial capacity is also influenced by the ratio between base-load plant and peak-load plant. In addition, we investigate how time lag between investment and operation influences the investment rule.

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.

Portfolio Optimization in Incomplete Markets

2019 ◽  
pp. 426-435
Author(s):  
Tomas Björk
Keyword(s):  
Portfolio Optimization ◽  
Incomplete Markets ◽  
Duality Theory ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Finite Sample ◽  
Martingale Approach ◽  
Dual Approach ◽  
Full Theory ◽  
Optimal Investment Problem

The object of this chapter is to give an overview of the dual approach to portfolio optimization in incomplete markets. The main result of this theory is that to every optimal investment problem there is a dual problem where we minimize a dual objective function over the class of martingale measures. For the case of a finite sample space we can present the full theory, but for the general case we only outline the proof. The theory is closely connected to convex duality theory and to the martingale approach to optimal consumption/investment discussed in Chapter 27.

scholarly journals An error-based active disturbance rejection control with memory structure

2020 ◽  
pp. 002029402091521 ◽  
Author(s):  
Sen Chen ◽  
Zhixiang Chen ◽  
Zhiliang Zhao
Keyword(s):  
Disturbance Rejection ◽  
Reference Signal ◽  
Memory Structure ◽  
Necessary Condition ◽  
Control Input ◽  
Active Disturbance Rejection Control ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control ◽  
Input Gain ◽  
With Memory

The paper studies the control problem for nonlinear uncertain systems with the situation that only the current reference signal is available. By constructing a memory structure to save the previous reference signals, a novel error-based active disturbance rejection control with an approximation for the second-order derivative of reference signal is proposed. The transient performance of the proposed method is rigorously studied, which implies the high consistence of the closed-loop system. More importantly, to attain the satisfactory tracking performance, the necessary condition for nominal control input gain is quantitatively investigated. Furthermore, the superiority of the proposed method is illuminated by contrastively evaluating the sizes of the total disturbance and its derivative. The proposed method can alleviate the burden of the estimation and compensation for total disturbance. Finally, the experiment for a manipulator platform shows the effectiveness of the proposed method.

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).

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