scholarly journals Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Gyoocheol Shim ◽  
Yong Hyun Shin
Keyword(s):  
Portfolio Choice ◽  
Optimization Problem ◽  
Absolute Risk ◽  
Programming Approach ◽  
Optimal Consumption ◽  
Choice Problem ◽  
Dynamic Programming Approach ◽  
Cara Utility ◽  
Constant Absolute Risk Aversion ◽  
Consumption Constraints

We consider the optimal consumption and portfolio choice problem with constant absolute risk aversion (CARA) utility and a subsistence consumption constraint. A subsistence consumption constraint means there exists a positive constant minimum level for the agent’s optimal consumption. We use the dynamic programming approach to solve the optimization problem and also give the verification theorem. We illustrate the effects of the subsistence consumption constraint on the optimal consumption and portfolio choice rules by the numerical results.

scholarly journals AN OPTIMAL CONSUMPTION AND INVESTMENT PROBLEM WITH QUADRATIC UTILITY AND SUBSISTENCE CONSUMPTION CONSTRAINTS: A DYNAMIC PROGRAMMING APPROACH

2018 ◽  
Vol 23 (4) ◽  
pp. 627-628 ◽  
Author(s):  
Yong Hyun Shin ◽  
Jung Lim Koo ◽  
Kum Hwan Roh
Keyword(s):  
Dynamic Programming ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Dynamic Programming Method ◽  
Programming Approach ◽  
Optimal Consumption ◽  
Dynamic Programming Approach ◽  
Investment Problem ◽  
Optimal Consumption And Investment ◽  
Consumption Constraints

In this paper, we analyze the optimal consumption and investment problem of an agent who has a quadratic-type utility function and faces a subsistence consumption constraint. We use the dynamic programming method to solve the optimization problem in continuous-time. We further provide the sufficient conditions for the optimization problem to be well-defined.

scholarly journals Effort, Idiosyncratic Risk and  Investment Under Uncertainty

2021 ◽  
Author(s):  
◽  
William S Taylor
Keyword(s):  
Risk Aversion ◽  
Executive Compensation ◽  
Absolute Risk ◽  
Investment Decisions ◽  
Idiosyncratic Risk ◽  
Capital Costs ◽  
Huge Impact ◽  
Uncertain Payoffs ◽  
Cara Utility ◽  
Constant Absolute Risk Aversion

<p>This thesis is based upon four very simple premises: 1. managers, not shareholders make the investment decisions for the firm; 2. managers do more than just say "yes" or "no" to investments, they can also exert effort that affects the payoff from investment; 3. executive compensation schemes can cause managers to hold more stock than is optimal for diversification purposes; and 4. many investments can be delayed and involve irreversible capital costs as well as uncertain payoffs. Combining these four premises gives the two central questions this thesis attempts to answer: 1. How does the level of managerial stock-ownership affect the investment decisions managers make for the firm? and 2. given the answer to (1), how does this affect the shareholder's decision to hire a manager? In this thesis I use a continuous time "Real Options" framework to answer these questions. The form of the utility function assumed for the manager has a huge impact on the tractability of the modelling. The assumption of Constant Relative Risk Aversion (CRRA) utility as opposed to Constant Absolute Risk Aversion (CARA) causes the manager's valuation of the cash  flow (the very first step of the modelling) to become wealth dependent. This in itself is an interesting issue, but it also poses interesting numerical issues and makes the later steps of the analysis intractable. Because of this we split the substantive analysis of this thesis into two parts. In the first we assume CARA utility in order to remove wealth dependence from the valuation and obtain a "clean path" to the end goal of a dynamic model of hiring, effort and irreversible investment. In the second we focus on CRRA utility thus allowing the manager's valuation to depend on his financial wealth. We then explain the resultant numerical issues, and the appropriate approach to their solution.</p>

scholarly journals A Novel Dynamic Programming Approach for Optimizing Driving Strategy of Subway Trains

2020 ◽  
Vol 325 ◽  
pp. 01002
Author(s):  
Hao Gao ◽  
Yadong Zhang ◽  
Jin Guo
Keyword(s):  
Dynamic Programming ◽  
Optimization Problem ◽  
Cost Functions ◽  
Programming Approach ◽  
Safe Driving ◽  
Dynamic Programming Approach ◽  
Urban Rail ◽  
Rail Line ◽  
Optimal Driving

The reduction of operation energy consumption without decreasing service quality has become a great challenge in subways daily operation. A novel DP based approach is proposed for optimizing the train driving strategy. The optimal driving problem is first considered as a multi-objective problem with five optimal targets (i.e., energy saving, punctual arriving, less switching, safe driving and accurate stopping). The optimization problem is remodelled as a multistage decision problem by discretizing the continuous train movement in space. The process of dynamic programming is carried out in the velocity-space status space. Due to the discretizing rules of searching space, the optimal goals of safe driving and accurate stopping can be satisfied during the searching process. The rest of multiple goals are spilt into cost functions and constrains for each stage. Due to the multiple cost functions, a set of pareto optimal solutions can be achieved at each vertex during the process of dynamic programming. To further improve the efficiency of algorithm, two evaluation criterions are introduced to maintain the capacity of the pareto set at each vertex. A case study of Yizhuang urban rail line in Beijing is conducted to verify the effectiveness and the efficiency of DP based algorithms.

Portfolio Choice

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Choice Model ◽  
Absolute Risk ◽  
Risk Tolerance ◽  
Absolute Risk Aversion ◽  
Initial Wealth ◽  
Optimal Investments ◽  
Mean Variance ◽  
Constant Absolute Risk Aversion

The portfolio choice model is introduced, and the first‐order condition is derived. Properties of the demand for a single risky asset are derived from second‐order risk aversion and decreasing absolute risk aversion. Optimal investments are independent of initial wealth for investors with constant absolute risk aversion. Optimal investments are affine functions of initial wealth for investors iwth linear risk tolerance. The optimal portfolio for an investor with constant absolute risk aversion is derived when asset returns are normally distributed. Investors with quadratic utility have mean‐variance preferences, and investors have mean‐variance preferences when returns are elliptically distributed.

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