scholarly journals Optimal Investment with Bounded VaR for Power Utility Functions

2014 ◽  
pp. 103-116
Author(s):  
Bénamar Chouaf ◽  
Serguei Pergamenchtchikov
Keyword(s):  
Optimal Investment ◽  
Utility Functions ◽  
Power Utility

scholarly journals An Optimal Investment Returns with N-Step Utility Functions

2016 ◽  
Vol 16 ◽  
pp. 96-104
Author(s):  
Joseph Thomas Eghwerido ◽  
Titilola Obilade
Keyword(s):  
Utility Function ◽  
Capital Market ◽  
Optimal Investment ◽  
Utility Functions ◽  
Design Parameters ◽  
Square Root ◽  
Power Utility ◽  
Market Structures ◽  
Investment Returns ◽  
Negative Exponential

In this paper, we shall validate the optimal payoff of an investment with an N-step utility function, [6, 7], such that H* is the payoff at time N in every possible state say 2n; in an N period market setting. Negative exponential, logarithm, square root and power utility functions were considered as the market structures change according to a Markov chain. These models were used to predict the performances of some selected companies in the Nigeria Capital Market. The estimates for models design parameters p, q, p', q' correspond to halving or doubling of investment. The performance of any utility function is determined by the ratio q: q' of the probability of rising to falling as well as the ratio p: p' of the risk neutral probability measure of rising to the falling.

scholarly journals Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Regime Switching ◽  
Stock Price ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Power Utility ◽  
Optimal Investment Strategy ◽  
Admissible Strategies ◽  
Definition Of ◽  
Markovian Regime Switching ◽  
Optimal Investment And Consumption

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

scholarly journals Legendre Transform-Dual Solution for a Class of Investment and Consumption Problems with HARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Absolute Risk ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Power Utility ◽  
Transform Method ◽  
Intermediate Consumption ◽  
Special Cases ◽  
Hara Utility ◽  
Optimal Investment And Consumption

This paper provides a Legendre transform method to deal with a class of investment and consumption problems, whose objective function is to maximize the expected discount utility of intermediate consumption and terminal wealth in the finite horizon. Assume that risk preference of the investor is described by hyperbolic absolute risk aversion (HARA) utility function, which includes power utility, exponential utility, and logarithm utility as special cases. The optimal investment and consumption strategy for HARA utility is explicitly obtained by applying dynamic programming principle and Legendre transform technique. Some special cases are also discussed.

Optimal asset allocation in retirement planning: threshold-based utility maximization

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Maximilian Bär ◽  
Nadine Gatzert ◽  
Jochen Ruß
Keyword(s):  
Interest Rates ◽  
Asset Allocation ◽  
Expected Utility Theory ◽  
Retirement Planning ◽  
Utility Functions ◽  
Market Model ◽  
Power Utility ◽  
Content Type ◽  
Retirement Saving ◽  
Saving Decisions

PurposeThe aim of this paper is to modify the shape of utility functions traditionally used in expected utility theory (EUT) to derive optimal retirement saving decisions. Inspired by current reference point based approaches, the authors argue that utility functions with jumps or kinks at certain threshold points might very well be rational.Design/methodology/approachThe authors suggest an alternative to typical utility functions used in EUT, to be applied in the context of retirement saving decisions. The authors argue that certain elements that are used to model biases in behavioral models should–in the context of optimal retirement saving decisions–be considered “rational” and hence be included in a normative setting as well. The authors compare the optimal asset allocation derived under such utility functions with results under traditional power utility.FindingsThe authors find that the considered threshold levels can have a significant impact on the optimal investment decision for some individuals. In particular, the authors show that a much riskier investment than under EUT can become optimal if some level of income is secured by a social security and a significant portion of the distribution of terminal wealth lies below this level.Originality/valueContrary to previous work, this model is especially designed to assess the question of optimal product choice/asset allocation in the specific setting of retirement planning and from a normative point of view. In this regard, the authors first motivate the use of several thresholds and then apply this approach in a capital market model with stochastic stocks and stochastic interest rates to two illustrative investment alternatives.

scholarly journals Portfolio optimization with unobservable Markov-modulated drift process

2005 ◽  
Vol 42 (2) ◽  
pp. 362-378 ◽  
Author(s):  
Ulrich Rieder ◽  
Nicole Bäuerle
Keyword(s):  
Portfolio Optimization ◽  
Drift Rate ◽  
Optimization Problems ◽  
Optimal Investment ◽  
Power Utility ◽  
Portfolio Strategy ◽  
Markov Modulated ◽  
Hamilton Jacobi Bellman ◽  
The Value Function ◽  
Complete Observation

We study portfolio optimization problems in which the drift rate of the stock is Markov modulated and the driving factors cannot be observed by the investor. Using results from filter theory, we reduce this problem to one with complete observation. In the cases of logarithmic and power utility, we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case, we investigate the so-called Bayesian case, i.e. where the drift rate is unknown but does not change over time. In this case, we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to that in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.

scholarly journals OPTIMAL INVESTMENT AND CONSUMPTION WITH STOCHASTIC FACTOR AND DELAY

2019 ◽  
Vol 61 (1) ◽  
pp. 99-117 ◽  
Author(s):  
L. LI ◽  
H. MI
Keyword(s):  
Optimal Strategies ◽  
Optimal Investment ◽  
Risky Asset ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Power Utility ◽  
Differential Delay Equation ◽  
Price Process ◽  
Stochastic Factor ◽  
Optimal Investment And Consumption

We analyse an optimal portfolio and consumption problem with stochastic factor and delay over a finite time horizon. The financial market includes a risk-free asset, a risky asset and a stochastic factor. The price process of the risky asset is modelled as a stochastic differential delay equation whose coefficients vary according to the stochastic factor; the drift also depends on its historical performance. Employing the stochastic dynamic programming approach, we establish the associated Hamilton–Jacobi–Bellman equation. Then we solve the optimal investment and consumption strategies for the power utility function. We also consider a special case in which the price process of the stochastic factor degenerates into a Cox–Ingersoll–Ross model. Finally, the effects of the delay variable on the optimal strategies are discussed and some numerical examples are presented to illustrate the results.

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